Unit 5 Review

Today, I want to work through each learning goal together to review for your test!

(Tip: Click here to open Desmos in another tab)

We have Finished Unit 5: Functions!!

Goal 7: I can Apply the concept of a function to analyze and solve problems.

Learning Target 7A:

I can determine if a relationship between two sets of values is a function.

(Lesson 1)

Look across the graph and make sure every x only has one y.

GRAPHS

Any time you are given a collection of input and output values, check that no input (x) repeats.

IF the x repeats, make sure it repeats the same y.

If one x value has different y-values, it is NOT a function!

Points / Tables / Maps

​​A relation is a function if every _________ only has ___ _________.

Multiple Choice

Is this a function or not a function? 

• Function
• Not a Function 

Multiple Choice

Is the relation a function? 
{(4,5), (4,-7), (4,2), (4,0), (4,9)}

• Yes
• No

Multiple Choice

Is this table a function or not a function? 

• Function
• Not a Function

Multiple Choice

Is the relation a function? Why.

• Yes, because the x-value 11 has two y-values pair with it.
• Yes, because each x-value has only one y-value paired with it.
• No, because the x-value 11 has two y-values pair with it.
• No, because each x-value has only one y-value paired with it.

Multiple Choice

It is a function?

• Yes

• No

Multiple Choice

It is a function?

• Yes

• No

Goal 7: I can Apply the concept of a function to analyze and solve problems.

Learning Target 7B:

I can use and interpret function notation appropriately.

(Lesson 3)

​Function notation:

Once you know what you are given (x or y) and what you need to find, you can use Desmos to help you!

Math Response

Given $$f\left(x\right)=-3x+10$$ , find $$f(7)$$ . (Hint: you can type it in Desmos to get the answer!)

Type answer here

Correct Answer: -11

Deg^°

Rad

Multiple Choice

What is f(8)? 

• 8
• 0
• 3
• -2

Multiple Choice

$$f\left(x\right)\ =\ 3\left(3x\ -7\right)$$

If f(x) = 24, what is the value of x?

• $$x\ =\ -9$$  

• $$x\ =\ 5$$  

• $$x\ =3$$  

• $$x\ =\ 7$$  

Multiple Choice

The function h(t) represents the height in inches of a plant after t weeks. What does the statement h(4) = 5 mean?

• After 5 week the plant is 4 inches tall
• The plant grows at a rate of 5/4 inch per week
• After 4 weeks the plant is 5 inches tall
• The plant grows at a rate of 1 inch per week

Goal 7: I can Apply the concept of a function to analyze and solve problems.

Learning Target 7c:

I can solve problems in context using a table/graph of a function.

(Lesson 6)

Labeling

Label the graph to the right with the following features:

Drag labels to their correct position on the image

6 seconds after it is launched

The highest point the rocket reaches.

When the rocket is launched into the air

When the rocket lands on the ground

Goal 7: I can Apply the concept of a function to analyze and solve problems.

Learning Target 7d:

I can find the values of a function given a rule and connect them to the graph of the function.

(Lesson 5)

Multiple Choice

Given the functions, which has the smallest output with an input of $$x=-24$$ ?
(Substitute x=-24 into each on Desmos and see which is biggest)

• f(-24)

• g(-24)

• h(-24)

• They all match

Multiple Choice

Given the functions, which has the greatest output from an input of x=10?

• f(10)

• g(10)

• h(10)

• They all match

Goal 8:  
I can identify key features of a function
and interpret them in terms of the context.

Goal 8: I can identify key features of a function and interpret them in context.

Learning Target 8a:

I can describe an interval where a function is increasing or decreasing and where it is positive or negative.

Your job is to find the input values where the output values are increasing or decreasing.

Increasing, decreasing

Your job is to find the input values that have either positive or negative output values.

positive, negative

​positive y-values

​Negative y-values

Match

Match the following intervals to when the graph is increasing, decreasing, or constant.

• Increasing

• Decreasing

• Constant

• $$0<x<10$$

• $$20<x<30$$

• $$10<x<20$$

Multiple Choice

For what interval of x is f(x) negative?

• x<-7 and x>3
• -7<x<3
• x>1
• x<-6

Multiple Select

For what intervals of x is f(x) positive? (There are two!)

• -7<x<2

• 0<x<4

• 5<x<7.5

• -6<x<-1

Goal 8: I can identify key features of a function and interpret them in context.

Learning Target 8b:

I can identify intercepts from a table or a graph and interpret them in terms of a context.

• Find the output from an input of ZERO.

• In a story: Usually our first output - "starting height" or "starting price"

• Remember! Vertical: Up & Down

Vertical Intercept

• Find the input(s) where the output is ZERO.

• In a story: Usually "touches the ground" or "makes no money"

• Remember! Horizontal: Left & Right

Horizontal Intercept

​X	​Y
​-1	​5
0​	3​
1​	-4​
2​	0​

Labeling

Label the graph's vertical and horizontal intercepts

Drag labels to their correct position on the image

Horizontal Intercept

Vertical Intercept

Dropdown

The vertical intercept of the graph is ​

Select answer

. This means that if we wait ​​

Select answer

hours, the starting temperature would be ​

Select answer

degrees.

Dropdown

The horizontal intercept is at ​

Select answer

. This means after ​

Select answer

seconds, the rocket is ​

Select answer

feet above the ground. This means it ​

Select answer

here.

Goal 8: I can identify key features of a function and interpret them in context.

Learning Target 8c:

I can sketch graphs showing key features given a verbal description in context.

Reorder

Put the parts of the story in order according to the graph.

• They start filling the empty tub

• The tub starts to drain a little for 3 minutes

• They continue filling up the tub

• The bathtub stays full for 5 minutes

• They drain the tub quickly

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Goal 8: I can identify key features of a function and interpret them in context.

Learning Target 8D:

I can relate the domain and range of a function to its graph, and to the relationship it describes.

Multiple Choice

All of the y values or outputs are called what?

• Domain
• Range
• Relation
• Function

Multiple Choice

All of the input values (usually x) are called what?

• Domain
• Range
• Relation
• Function

Multiple Choice

Identify the domain of the following relation:

• $$-6\le x\le4$$

• $$(-6,14)\ (0,32)\ (2,38)\ (4,44)$$

• $$\left\{-6,0,2,4\right\}$$

• $$\left\{14,32,38,44\right\}$$

Multiple Choice

Identify the range of the following relation:

• 14 < y < 44

• {(-6,14), (0,32), (2,38), (4,44)}
• {-6, 0, 2, 4}
• {14, 32, 38, 44}

Match

Match the following

• Integers

• Whole Numbers

• Real Numbers

-3, -1, 0, 4, 17

0, 5, 24

-3, 1/2, 0, 2.79, 450

• -3, -1, 0, 4, 17

• 0, 5, 24

• -3, 1/2, 0, 2.79, 450

Dropdown

Your paycheck is a function of the hours you work. The domain for this would represent the ​

Select answer

you work and would be ​

Select answer

​

Select answer

.

Dropdown

Your paycheck is a function of the hours you work. The range for this would represent the ​

Select answer

and would be ​

Select answer

​

Select answer

.

Dropdown

The domain of this function represents ​

Select answer

and can be described as ​

Select answer

numbers from ​

Select answer

to ​

Select answer

.

Dropdown

The range of this function represents ​

Select answer

and can be described as some ​

Select answer

numbers from ​

Select answer

to ​

Select answer

.

Goal 8: I can identify key features of a function and interpret them in context.

Learning Target 8E:

I can calculate and interpret the average rate of change for a function over a specified interval.

We use "average" when we describe a rate of change that is not constant.

"Average" rate of change is just like linear rate of change!

Multiple Choice

Find the rate of change between the points (2, 4) and (6, 12)

• 1/2
• -1/2
• 2
• -2

Multiple Choice

Calculate the average rate of change from 20 to 40 minutes.

• -2 minutes per gallon

• -20 minutes per gallon

• -2 gallons per minute

• -20 gallons per minute

Multiple Choice

What is the rate of change of c(x) when 1 < x < 3

• 4
• 5
• 2
• 1

Multiple Choice

The table below shows the snowfall in inches for the first week in January. Find the average rate of change in the number of inches of snowfall from January 8 (1/8) to January 11 (1/11).

• An average increase of 2/3 inches per day

• An average increase of 2 inches per day

• An average decrease of 2/3 inches per day

• An average increase of 3/2 inches per day