FUNCTIONS RETAKE REVIEW

​Must pass the vertical line test

​From a graph

​

1. The equation can be written as y= mx+b

2. ​The exponent on x must be 1.

​

​FROM AN EQUATION

​Identifying Functions

Some text here about the topic of discussion

Draw

Does this relation define a function?

A table represents a function when each input has exactly one output. (the x-value does not repeat)​

From a table

A relation is a function when the x-values (input) are all different.

From a relation

I can Identify a function

Some text here about the topic of discussion

Multiple Select

Select all of the relations that represent a function. 

• $$\left\{\left(1,-3\right)\left(4,-5\right)\ \left(2,\ 2\right)\left(1,\ 9\right)\right\}$$  

• $$\left\{\left(3,\ 3\right),\ \left(4,\ 4\right),\ \left(5,\ 5\right),\ \left(6,\ 6\right)\right\}$$  

• $$\left\{\left(1,\ -2\right)\ \left(-3,\ \ 4\right)\ \left(-1,\ 8\right)\ \left(-3,\ 2\right)\right\}$$  

• $$\left\{\left(3,2\right)\left(-8,\ 2\right)\ \left(-10,\ 2\right)\left(5,\ 2\right)\right\}$$  

​The slope is also called the rate of change.

​​ Slope and Y-intercept from an equation.

​

​Find where your input (x) is equal to zero. Sometimes you may have to calculate it. Y-intercept is (0,5). The slope/rate of change is 5/1 or 5.

​​Y-intercept and slope from a table

​

​The y intercept is where the line crosses the y-axis. The slope is calculate by rise/run.

​​Y intercept and slope from a graph.

​

Draw

Circle the y intercept. Write it as an ordered pair.

Multiple Choice

What is the y-intercept of this equation?

• $$\left(0,6\right)$$  

• $$\left(6,0\right)$$  

• $$\left(0,3\right)$$  

• $$\left(3,0\right)$$  

Open Ended

Write the equation for the following verbal equation:

The variable y is 2 more than 4 times x.

Multiple Choice

What is the y-intercept for the equation:

y is 2 more than 4 times x.

• (0,2)

• (0,4)

• (4,2)

• (2,4)

Multiple Choice

Compare the last two functions- the graph to the left and function B:

the equation y is 2 more than 4 times x.

Describe their y-intercepts.

• The y intercept of function A is twice the y intercept of function b

• The y intercept of function A is the same as the y intercept of function b

• The y intercept of function A is one less than the y intercept of function b

• The y intercept of function A is one more than the y intercept of function b

The equation can be written in y=mx+b and the exponent on the variable must be 1.

​​Linear function from an equation.

​

​A table represents a linear function when the input is changing by the same amount and the output is changing by the same amount. We call this constant rate of change.

​​Linear from a table

​

​The graph is a straight line.

​​Linear from a graph.

​

Multiple Choice

Which of the following equations does not represent a linear relationship between x and y?

• $$y=4x$$  

• $$y=2x^2\ +5x$$   

• $$5x=3\left(y-2\right)$$  

• $$6x-7y=13$$  

Multiple Choice

Bacteria grow in colonies over time. Which table shows growth of bacteria colonies that can be modeled by a linear graph?

Open Ended

Does the following scenario represent a function? Why or why not?

The total cost of a large pizza based on $9.95 plus $0.75 for each additional topping.

Open Ended

Does the following scenario represent a function? Why or why not?

The ant population for a colony that begins with 5 ants and doubles in number every two weeks.

Open Ended

Does the following scenario represent a function? Why or why not?

The amount of gasoline in a vehicle that begins with 22 gallons and decreases by one gallon every 28 miles.

Open Ended

Does the following scenario represent a function? Why or why not?

A history student's grade on a test that begins at 100 but decreases by 4 points for each question answered incorrectly.

Draw

Arya runs a landscaping business. She charges based on the equation y= 15x + 30. Fill in the table for Arya.

Draw

Cody also runs a landscaping business. What is Cody's initial value and rate of change? What does Cody charge per hour?

Multiple Choice

Looking at Cody and Arya, who charges more per hour?

• Cody charges $5 more per hour

• Arya charges $5 more per hour

• They charge the same amount.

• Aria charges $10 less per hour.

Fill in the Blanks

When the input of the function is -3, what is the output of the function?

Draw

When the input of this function is 4, what is the output

Multiple Choice

A function is given by the equation $$ax^b+c$$   where a, b and c are constants. What values of a, b and c make this function linear?

• a=1, b=2, c=0

• a= 4, b= -1, c=2

• a= -1, b=1, c= 4

• a= 4, b=-2, c=-2

Draw

Find the rate of change of each function.

Open Ended

The rate of change of function 2 is ____ times greater than function 1.

Reorder

Reorder the following from least to greatest

1

2

3

• 1
• 2
• 3