Learning activity 1.1: Introducing functions

In grades 9 and 10 you learned about linear and quadratic relations. In this course you will broaden your understanding by learning about a group of relations called functions. You will also expand your mathematical vocabulary to include new ways to describe relations, including stating the domain and range, which describe where, on the Cartesian plane, you will see points on the graph of a relation. You will also represent relations using mapping diagrams, graphs and tables of values.

We are going to start by defining the term relation.

After watching the video, take a few minutes to answer the following questions:

Without looking at the video again, can you recall how many ways there are to express a relation? List the ones you remember.

Student Answer

There are 7 ways of expressing a relation.

List of ordered pairs
Mapping diagram
Table
graph
Equation
Words
Rule

Which ways are most familiar to you?

Student Answer

Multiple answers are possible.

Common answer: Table, graph and equation.

Which ways are least familiar to you?

Student Answer

Multiple answers are possible.

Common answer: Mapping diagram

Note
This learning activity will help you better understand the various ways of expressing relations.

A relation is an expression that demonstrates the connection (relationship) between two variables: an independent variable (x) and a dependent variable (y).
The expression can be in the form of a set of ordered pairs, a mapping diagram, a table of values, a graph, an equation, a description in words, or a rule.

Set of ordered pairs

${(0,1), (1, 2), (2, 3), (3, 4), (4,5)}$

Mapping diagram

Table of values

x	y
1	1
2	4
3	9
4	16
5	25

Graph

Description in words or a rule

To fix a car, TJ’s Garage charges a base fee of $20, plus $40 for each hour of labour.

Now let’s build up on our knowledge of relations by analyzing the examples below:

Example 1
Example 2

Example 1

To fix a car, TJ’s Garage charges a base fee of $20, plus $40 for each hour of labour.

This is an example of a relation because it is a description of the relationship between the total cost to fix a car and the number of hours of labour. This relation can also be expressed in the form of a set of ordered pairs, a mapping diagram, a table of values, a graph, an equation, or a rule.

Take a minute to review the different forms for expressing relations. Identify three different forms in which this relation could be expressed.

Suggestions

Equation

Table

Graph

Example 2

Mina recorded the ages and heights of her cousins and presented the information in the form of a table below.

The table is an example of a relation because it represents the relationship between age and height of each person.

Age	Height in centimeters
15	152
15	185
16	155
17	170
17	173
18	185
20	161

Look carefully at the two examples of relations. What is same? What is different?

Student Answer

Example 1 is in words and example two is a table of values. Both examples are examples of relations. In the second relation, two heights (dependent variable) are associated with a single age (independent variable). For example, heights of 152 cm and 185 cm are associated with 15 years of age.

The difference between the two relations brings us to the definition of a special type of relation called a function.

Definition

A function is a relation where each value of the independent variable $x$ corresponds to only one value of the dependent variable $y$ (no repeated $x$ values, but it’s okay for the $y$ values to be repeated).

Let’s revisit our two examples of relations.

Example 1
Example 2

Example 1

To fix a car, TJ’s Garage charges a base fee of $20, plus $40 for each hour of labour.

This is an example of a relation that is also a function because each value of time is mapped onto only one value of total cost.

The total cost depends on the number of hours of labour. Each value of the independent variable (hours of labour) correspond to only one value of the dependent variable (total cost). Therefore, the relation is a function.

The diagram shown here is called a mapping diagram. The number of hours is mapped onto the total cost.

The total cost depends on the number of hours of labour, therefore we can conclude that the independent variable is the number of hours and the dependent variable is the total cost. You can see that each value for the number of hours maps onto only one value for total cost.

Example 2

Mina recorded the ages and heights of her cousins and presented the information in the form of a table below.

This relation is not a function because the age 15 for example is mapped onto two different heights and the same applies to an age of 17. This tells us that one independent value corresponds to more than one dependent value.

Age	Height in centimeters
15	152
15	185
16	155
17	170
17	173
18	185
20	161

In conclusion, a relation can be further classified as a function if there is only one value of the dependent variable for each value of the independent variable.

A function in the form of an equation can be expressed using what we call function notation.

With function notation, we replace $y$ with $f (x)$ , read as “ $f$ at $x$ ” or “ $f$ of $x$ ”
$f (x)$ means “the value of the dependent variable for a specific value of $x$ ”
It means that we are expressing an equation as a function in terms of $x$
It means that $y = f (x)$

Take a minute to watch the video below to learn about the advantage of using function notation:

Now let’s re-visit example 1 and make an equation for the function, and then express it using function notation.

What steps should I take?

Step 1: Define the variables

Let $x$ represent the number of hours of labour and $y$ represent the total cost.

Step 2: Write the equation

To fix a car, TJ’s Garage charges a base fee of $20, plus $40 for each hour of labour.

This is a linear relationship, which means that the equation will be in the form

$y = m x + b$

where $y$ represents the total cost to get a car fixed, m (rate) is the cost per hour, $x$ is the number of hours and b is the base fee

therefore: $x$ and $y$ are variables, so we keep them the same in the general equation

$m = 40$ and $b = 20$

The equation is $y = 40 x + 20$

To write the equation using function notation, we replace $y$ with $f (x)$ .

Therefore, $y = 40 x + 20$ in function notation becomes $f (x) = 40 x + 20$

What do you think is the meaning of $f (3) = 140$ ?

$f (3) = 140$ means that when $x = 3, y = 140$ . If you were to sketch the graph of

$f (x) = 40 x + 20$ , the point (3, 140) is one of the points on the graph.

In example 2, Mina recorded the ages and heights of her cousins and presented the information in the form of a table on the right.

Can we express this relation using function notation?

No. The relation above is not a function, therefore it cannot be expressed using function notation.

Age	Height in centimeters
15	152
15	185
16	155
17	170
17	173
18	185
20	161

Domain and Range

Key features of all relations are domain and range.

the domain is the set of all possible values of the independent variable
the range is the set of all possible values of the dependent variable

Let’s use our two examples to practice stating the domain and range

Example 1
Example 2

Example 1:

To fix a car, TJ’s Garage charges a base fee of $20, plus $40 for each hour of labour.

The independent variable is time (x) since the total cost depends on the number of hours. In reality, we cannot have negative time, hence we can conclude that the lowest value of time that would make sense in this situation is 0 and the maximum time is unlimited.

The domain for this example can be stated in words or in mathematical symbols:

Domain = {x is an element of the real numbers, such that $x$ is greater than or equal to zero}

Notation
$x$ is an element of real numbers: $x \in R$
such that:
$x$ is greater than or equal to zero: $x \geq 0$
Using symbols, this becomes $D = \{x \in R| x \geq 0\}$

The dependent variable is the total cost ( $y$ ) since the total cost depends on the number of hours. The lowest cost in this situation is $20 since the base fee is $20 and the total cost is unlimited.

The range for this example can be stated as:
Range = { $y$ is an element of real numbers such that, $y$ is greater than or equal to 20}

Notation
$y$ is an element of real numbers: $y \in R$
such that:
$y$ is greater than or equal to 20: $y \geq 20$
Using symbols, this becomes $R = \{y \in R| y \geq 20\}$

Example 2:

Mina recorded the ages and heights of her cousins and presented the information in the form of a table below.

Age	Height in centimeters
15	152
15	185
16	155
17	170
17	173
18	185
20	161

The independent variable in this data is age, but this relation is different from the one above because it is limited to 7 specific pairs of points, hence the domain is a list of the ages.

The domain for this example is a list of the ages and the repeated ages should be represented only once and listed from least to greatest.

Domain = {15, 16, 17, 18, 20}

The dependent variable in this data is height, but this relation is different from the one above because it is limited to 7 specific pairs of points, hence the range is a list of the heights.

The range for this example is a list of the heights and the repeated heights should be represented only once and listed from least to greatest.

Range = {152, 155, 161, 170, 173, 185}

Examples

Example 1:

For the following set of ordered pairs: {(-2,5), (0,11), (0,8), (3,0) (4,-1)}

State the domain and range.

Since these are points, we state the domain by listing the $x$ - coordinates from least to greatest and if a number is repeated, we write it only once

Domain = { -2, 0, 3, 4} Note: 0 is repeated, but we only represent it once

Since these are points, we state the range by listing the $y$ - coordinates from least to greatest and if a number is repeated, we write it only once

Range = { -1, 0, 5, 8, 11}

Does the relation define a function? Explain your reasoning.

The relation is not a function because $x = 0$ is mapped onto 2 different $y$ values (x = 0 is repeated)

Example 2:

For the following set of ordered pairs: {(13,1), (-2, 5), (-7,4), (3,2) (9,-1)}

State the domain and range.

Since these are points, we state the domain by listing the $x$ - coordinates from least to greatest and if a number is repeated, we write it only once

Domain = { -7, -2, 3, 9, 13}

Since these are points, we state the range by listing the $y$ - coordinates from least to greatest and if a number is repeated, we write it only once

Range = { -1, 1, 2, 4, 5}

Does the relation define a function? Explain you reasoning.

The relation is a function because each $x$ -value is mapped onto only one $y$ -value

(no repeated $x$ -values)

Example 3:

For the given table of values

x	y
1	1
2	4
3	9
4	16
5	25

State the domain and range.

Since these are points, we state the domain by listing the $x$ - coordinates from least to greatest and, if a number is repeated, we write it only once

Domain = {1, 2, 3, 4, 5}

Since these are points, we state the range by listing the $y$ - coordinates from least to greatest and if a number is repeated, we write it only once

Range = {1, 4, 9, 16, 25}

Does the relation define a function? Explain you reasoning.

The relation is a function because each $x$ -value is mapped onto only one $y$ -value

(no repeated $x$ -value)

Example 4:

For this mapping diagrams:

State the domain and range.

Since these are points, we state the domain by listing the $x$ - coordinates from least to greatest and if a number is repeated, we write it only once

Domain = {-2, 3, 7, 12}

Since these are points, we state the range by listing the $y$ - coordinates from least to greatest and if a number is repeated, we write it only once

Range = {11, 12, 14}

Does the relation define a function? Explain you reasoning.

The relation is a function because each $x$ – value is mapped onto only one $y$ -value (no repeated x-value)

Note: remember it’s okay to have one $y$ -value mapped on to 2 $x$ -values, but not the other way round

Example 5:

For this mapping diagram:

State the domain and range.

Since these are points, we state the domain by listing the $x$ - coordinates from least to greatest and if a number is repeated, we write it only once

Domain = {-7, -3, 1, 5}

Since these are points, we state the range by listing the $y$ - coordinates from least to greatest and if a number is repeated, we write it only once

Range = {2, 3, 7, 9}

Does the relation define a function? Explain you reasoning.

The relation is not a function because $x = 5$ is mapped onto two different $y$ -values

( $x = 5$ is repeated)

When given a graph, a quick way of determining whether a relation is a function is by carrying out a test called the vertical line test.

You imagine drawing vertical lines anywhere on the given graph. If the relation:

is not a function, the vertical line will pass through at least two points on the graph of the relation
is a function, the vertical line will pass through only one point on the graph of the relation

Let’s Practice

Question 1:

For the given graph

State the domain and range.

We state the domain by writing the interval for which the graph is defined. The circle lies between $x = - 3$ and $x = 3$ (inclusive)

Domain = { $x$ is an element of real numbers, such that $x$ lies between -3 and 3 inclusive}

Using symbols, this becomes $D = {x \in R | - 3 \leq x \leq 3}$

Hint
$x$ is an element of real numbers: $x \in R$
such that:
$x$ lies between -3 and 3 inclusive : $- 3 \leq x \leq 3$

We state the range by writing the interval for which the graph is defined. The circle lies between $y = -3$ and $y = 3$ (inclusive)

Range = { $y$ is an element of real numbers such that, $y$ lies between -3 and 3 inclusive}
Using symbols, this becomes $R = {y \in R | - 3 \leq y \leq 3}$

Hint
$y$ is an element of real numbers: $y \in R$
such that:
$y$ lies between -3 and 3 inclusive : $- 3 \leq y \leq 3$

Does the relation define a function? Explain you reasoning.

The relation is not a function because if I draw a vertical line anywhere on the circle, except at the $x$ intercepts, the vertical line will cross the circle twice

Question 2:

For the given graph

State the domain and range.

We state the domain by writing the interval for which the graph is defined. The graph lies between $x = - 4$ and $x = 4$ (inclusive)

Domain = {x is an element of real numbers, such that $x$ lies between -4 and 4 inclusive}

Using symbols, this becomes $D = \{x \in R| - 4 \leq x \leq 4\}$

Hint
$x$ is an element of real numbers: $x \in R$

such that:

x lies between -4 and 4 inclusive : $- 4 \leq x \leq 4$

We state the range by writing the interval for which the graph is defined. The graph lies between $y = 0$ and $y = 4$ (inclusive)

Range = {y is an element of real numbers such that, $y$ lies between -4 and 4 inclusive}

Using symbols, this becomes $R = {y \in R | 0 \leq y \leq 4}$

Hint
$y$ is an element of real numbers: $y \in R$

such that:

$y$ lies between 0 and 4 inclusive: $0 \leq y \leq 4$

Does the relation define a function? Explain you reasoning.

The relation is a function because, if I draw a vertical line anywhere on the relation, the vertical line crosses the relation only once.

Question 3:

For the given graph

State the domain and range.

We state the domain by writing the interval for which the graph is defined. The line passes through all values of x.

Domain = {x is an element of real numbers}

Using symbols, this becomes $D = \{x \in R\}$

Hint
$x$ is an element of real numbers: $x \in R$

We state the range by writing the interval for which the graph is defined. Once again, the line passes through all values of y.

Range = {y is an element of real numbers}

Using symbols, this becomes $R = \{y \in R\}$

Hint
$y$ is an element of real numbers: $y \in R$

Does the relation define a function? Explain you reasoning.

The relation is a function because if I draw a vertical line anywhere on the graph, the vertical line crosses the graph only once.

You can also recognize whether a relation is a function, or not, given its equation.

Linear relations with the general forms below are functions:
1. Slope y-intercept form: $y = m x + b$
2. Standard form: $A x + B y = C$ or $A x + B y + C = 0$

Quadratic relations with the general forms below are functions:
1. Standard form: $y = a x^{2} + b x + c$
2. Vertex form: $y = a (x - h)^{2} + k$
3. Factored form: $y = a (x - s) (x - t)$

Circles with the general forms below are not functions:
1. Centre at the origin: $r^{2} = x^{2} + y^{2}$
2. Centre at (a, b): $r^{2} = {(x - a)}^{2} + {(y - b)}^{2}$

Note:

Sometimes it is helpful to rearrange the equation of a relation to assess whether it is a function or not.

Examples:

Use your knowledge of equations to determine if the following relations are functions. Explain your thought process.

$y = 4 x + 3$

This is a linear function because it is in the form $y = m x + b$

$y = 2 - x$

$y = 2 - x$ can be rearranged to $y = - x + 2$

This is a linear function because it is expressed in the form $y = m x + b$

$y = 5 x^{2} - 9 x + 20$

This is a quadratic function in standard form because it is expressed in the form

$y = a x^{2} + b x + c$

$y = - 11 (x + 8)^{2} + 33$

This is a quadratic function in vertex form because it is expressed in the form
$y = a (x - h)^{2} + k$

$y = 33 + 9 (x - 4)^{2}$

Hint: $y = 33 + 9 (x - 4)^{2}$ can be rearranged to $y = 9 (x - 4)^{2} + 33$

This is a quadratic function in vertex form because it can be expressed in the form
$y = a (x - h)^{2} + k$

$y = - 5 (x - 3) (x + 4)$

This is a quadratic function in factored form because it can be expressed in the form

$y = a (x - s) (x - t)$

$25 = x^{2} + y^{2}$

This is not a function because it is a circle in the form $r^{2} = x^{2} + y^{2}$

$5 x^{2} + 7 y = 8$

Hint: $5 x^{2} + 7 y = 8$ can be expressed as $y = \frac{- 5}{7} x^{2} + \frac{8}{7}$

This is a quadratic function in standard form: $y = a x^{2} + b x + c$

Practice Questions

Notebook

Complete the questions that follow in your Notebook. When you are done, compare your work to the solutions given. If you have errors, identify them, write about them, and do the question again below your previous set of solutions.

Question 1
Question 2

Question 1:

For the function $f (x) = x^{2} + 10 x$ evaluate each of the following:

$f (7)$

$f (7)$ means replace $x$ with a 7 in the equation $f (x) = x^{2} + 10 x$

$f (7) = {(7)}^{2} + 10 (7)$

$= 49 + 70$

$= 119$

$f (2) + f (3)$

$\begin{array}{l} f (2) + f (3) = [{(2)}^{2} + 10 (2)] + \\ [{(3)}^{2} + 10 (3)] \end{array}$

\begin{array}{l} = (4 + 20) + (9 + 30) \\ = 24 + 39 \\ = 63 \end{array}

$2 f (4)$

$2 f (4) = 2 [{(4)}^{2} + 10 (4)]$

\begin{array}{l} = 2 (16 + 40) \\ = 2 (56) \\ = 112 \end{array}

Question 2:

If $f (x) = 11 x - 9$ , solve for $x$ if $f (x) = 2$ .

Replace $f (x)$ with a 2 and then isolate $x$ .

$2 = 11 x - 9$ add 9 to both sides of the equation

$2 + 9 = 11 x$

$11 = 11 x$ divide both sides of the equation by 11

$1 = x$

Therefore, $x = 1$ . When $x = 1$ , $y = 2$ , which means that the point (1, 2) is on the graph of

$f (x) = 11 x - 9$

Question 3:

For each of the following, determine whether, or not, the relation is a function. Explain your thought process.

{(1, 4), (2, 8), (3,16), (4,32)}

The relation is a function because there is no repeated $x$ – value.

{(3,0), (2, 13), (3,-9), (5,11)}

The relation is not a function because $x = 3$ is repeated in the points (3,0) and (3,-9).

The relation is a function because there is no repeated $x$ -value.

The relation is not a function because $x$ = 64 is repeated in the points (64,1) and (64,-8).

x	y
1	2
2	5
3	10
4	17
5	26

The relation is a function since there is no repeated $x$ -value

The relation is not a function because it fails the vertical line test (a vertical line drawn on the circle crosses it twice)

The relation is a function because it passes the vertical line test (a vertical line crosses the graph once)

$y = x^{2} + 100 x - 200$

The relation is a quadratic function in the form $y = a x^{2} + b x + c$

$y = 2 x - 23$

The relation is a linear function in the form $y = m x + b$

${625 = x}^{2} {+ y}^{2}$

The relation is not a function because it is an equation of a circle in the form

$r^{2} = x^{2} + y^{2}$

Self-Reflection

In this course you are an independent, self-directed learner. Consider this definition of a self-directed learner:

Definition

Self-directed learners are aware of how they learn best. They are confident and know when to ask for support. Self-directed learners set goals and make realistic plans to meet those goals. In other words, they make a commitment to their own learning and take responsibility for it.

As a self-directed learner, track your progress on the following:

I am able to:	All the time	Most of the time	Half the time	Struggling
explain the meaning of the terms relation and function.	1	2	3	4
explain the difference between a relation and a function.	1	2	3	4
determine whether a relation is a function or not, given: a set of ordered pairs; a mapping diagram; a table of values; using the vertical line test; using my general knowledge about relations.	1	2	3	4
represent functions algebraically using function notation.	1	2	3	4
use function notation to determine dependent variables for given independent variables given: a graph; an equation; a table.	1	2	3	4
explain the meaning of the terms domain and range.	1	2	3	4
determine the domain and range given: a set of ordered pairs; a mapping diagram; a table of values; a graph; using my general knowledge about relations.	1	2	3	4

Now take some time to review and reflect on the Learning goals and Success criteria in this Learning activity.

How would you rate your understanding of the concepts from this Learning activity? Check one.

I feel I have a thorough understanding of the concepts.

Awesome! Congratulations. You are ready to move on to the Next Steps.

I feel I have a considerable understanding of the concepts.

That’s great! Which concept are you concerned with? You are encouraged to go online and search for websites that provide extra practice. There are also websites that might have a video demonstration of a solution to a similar problem.

I feel I have a good understanding of the concepts.

Do you feel that some of these concepts are just hard concepts to grasp in general? Try to identify specific places where you could work to improve.

Go back and review the examples and exercises. You should also retry the practice questions.

I feel I have a limited understanding of the concepts.

Do you feel that some of these concepts are just hard concepts to grasp in general? Try to identify specific places where you could work to improve. You may want to review foundation skills that were presented in your Grade 10 course.

Try to work through the example and practice problems independently and then compare your solutions to those provided.

Based on your assessment, do you need more review? Additional practice can be found on the Centre for Education in Mathematics and Computing website, or by searching for resources using key words from the success criteria for this learning activity.

Culminating Activity

Part of the evaluation of this course will be in the form of a culminating activity, worth 10% of your final course work.

Throughout this course, you will learn about different types of functions, transformations and domain and range. For the culminating activity, you will use this knowledge to create a logo or picture that is informative or suggests solutions to problems that are contributing to environmental issues.

This culminating activity is an opportunity for you to showcase your knowledge of different types of functions and relations as well as your knowledge of domain and range.

The scenario

You are interviewing for a job in the marketing department of an environmental agency. As part of the application process you have been asked to develop a logo for an initiative that targets a specific environmental issue. The subject matter is your choice, but you must provide equations and limits to domain and/or range for each so a graphic designer who works for the organization could duplicate your logo.

Your logo or picture could be a way of:

educating people about environmental issues in the world at large;
drawing attention to specific environmental events (e.g. rising sea levels).
suggesting ways to reduce environmental impact.

Read the instructions for this assessment and the rubric that will be used to score it carefully. Pay close attention to the mathematical concepts that must be included. The checklist and rubric should serve as guides as you complete this activity.

Through the culminating activity, you are encouraged to translate your ideas into appropriate actions to make this world a better place. You are also encouraged to use technology to optimize your learning through technological innovations to deepen and transform your learning as you work on this activity.

Instructions

Identify the environmental issue that is the focus of your logo.
Create a picture or logo using the concepts of transformations, graphing, domain and range that were taught in this course. Use a minimum of four different types of functions as the key elements of your logo. You may also use relations, such as the inverses of functions or circles. Note that, at this point in the course, you have not learned many of these concepts.
Your logo must be displayed on a grid that shows the $x$ and $y$ axes with clear scales.

Incomplete example

First Key Element (Large Tree)

Equation: $y = - 2 {(x + 4.5)}^{2} + 4.5$

Restrictions on the domain: ${- 7 < x < - 3}$

Description of transformations: The parent function, $y = x^{2}$ has been stretched vertically by a factor of 2, reflected in the x-axis, translated left 4.5 units and translated up 4.5 units.

Second key element (Sides of the triangle)

Equation 1: $y = - x + 15$
Restrictions on the domain: ${1 \leq x \leq 22}$

Equation 2: $y = x + 13$
Restrictions on the domain: ${- 19 \leq x \leq 1}$

You may create your logo using pencil and paper or the graphing technology of your choice, such as Desmos or GeoGebra.
Describe how your logo relates to the issue that you have chosen.

For each element

Include an equation that defines it. With the exception of $f (x) = x$ , the equation should feature at least three transformations of the associated parent function.

Examples of parent functions are $f (x) = x$ , $f (x) = x^{2}$ , $f (x) = \sqrt{x}$ , $f (x) = \frac{1}{x}$ , $f (x) = \sin x$ and $f (x) = \cos x$

For each equation (with the exception of $f (x) = x$ ) describe the effects of each transformation on the parent function.
State the domain and range of each function or relation and the restrictions that were applied when constructing the logo. Use correct mathematical language and notation.

Remember: This culminating activity is an opportunity for you to showcase your knowledge of different types of graphs as well as your knowledge of domain and range.

I have identified an environmental issue and created a logo to effectively represent that issue by making connections between algebraic and graphical representations of functions.
I have created the logo on graph paper using correct mathematical form, including appropriate, clearly indicated scales.
I have described how the logo relates to the issue that was chosen.
I have used a minimum of four different types of functions or relations in my logo.
I have included an equation for each function that features a minimum of three transformations to modify the parent function.
I have described the three transformations that modified the parent function.
I have stated the domain and range of each function, using correct mathematical language and notation.
I have appropriately restricted the domain and/or range to support the construction of the logo.

Rubric

The teacher will assess your work using the following rubric. Before submitting your assessment, review the rubric to ensure that you are meeting the success criteria to the best of your ability.

Knowledge & Understanding

Success Criteria:

Displays logo as a well labelled graph

Level 4 80-100%	Level 3 70-79%	Level 2 60-69%	Level 1 50-59%
With high degree of effectiveness	With a considerable degree of effectiveness	With some degree of effectiveness	With limited effectiveness

Thinking

Success Criteria:

Determines 4 equations that model the graphical representations

Level 4 80-100%	Level 3 70-79%	Level 2 60-69%	Level 1 50-59%
With high degree of effectiveness	With a considerable degree of effectiveness	With some degree of effectiveness	With limited effectiveness

Application

Success Criteria:

Describes at least three transformations of the parent function
Determines domain and range for each transformed function

Level 4 80-100%	Level 3 70-79%	Level 2 60-69%	Level 1 50-59%
With high degree of effectiveness	With a considerable degree of effectiveness	With some degree of effectiveness	With limited effectiveness

Communication

Success Criteria:

Chooses an issue and describes how the logo relates to the issue
Uses mathematical language and notation

Level 4 80-100%	Level 3 70-79%	Level 2 60-69%	Level 1 50-59%
With high degree of effectiveness	With a considerable degree of effectiveness	With some degree of effectiveness	With limited effectiveness

Learning Goal

Success Criteria

Definition

What steps should I take?

Domain and Range

Examples

Let’s Practice

Practice Questions

Notebook

Self-Reflection

Definition

Culminating Activity

Rubric