3/28 Intro to Functions Quiz Review

Poll

While Everyone joins the game, answer this question: How familiar are you with functions?

• uh... What is a function?

• I have heard of them but know nothing about them

• I know a little bit about them

• I know everything there is to know about them

Function

• Definition: A relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

• Characteristic/Fact: A function is often in the form of y = x with some operation being performed on the x value

Input

• Definition: what is put in, taken in, or operated on by any process or system such as a function

• Characteristic/Fact: the input is all of the possible x values of a function. It is also called the domain.

Drag and Drop

A​

Placeholder

is a plane that is divided into 4 regions by a horizontal x-axis and vertical y-axis ​

Drag these tiles and drop them in the correct blank above

Coordinate Plane

x-axis

y-axis

Function

Dropdown

The ​

Select answer

is a value that is substituted for the independent variable in a function.

Drag and Drop

The ​

Placeholder

is the result of substituting a variable in a function.

Drag these tiles and drop them in the correct blank above

Output

Input

Function

Relation

Drag and Drop

The ​

Placeholder

is an algebraic expression that defines a function.

Drag these tiles and drop them in the correct blank above

Function Rule

Function

Domain

Range

Multiple Choice

A relation in which every input has only one output.

• relation

• function

• domain

• range

Dependent Variable vs Independent Variables

Example:

Sarah is participating in a walkathon to raise money for local literacy programs. The amount of money Sarah will raise depends on the distance she walks.

m = the amount of money Sarah will raise (DEPENDENT)

d = the distance Sarah walks (INDEPENDENT)

Match

Match the following using the phrase

"_____ depends on _____"

• your cell phone bill

• how far you can drive

• your math grade

• how much money you earn

• cost of a speeding ticket

minutes used

amount of gas you have

the number of assignments you turn in

the hours you work

how many miles you went over the speed limit

• minutes used

• amount of gas you have

• the number of assignments you turn in

• the hours you work

• how many miles you went over the speed limit

Multiple Choice

Identify the independent variable, dependent variable, and equation in function notation for the situation.

"An amusement park charges a $6.00 parking fee plus $29.99 per person. "

• Independent: Total Cost

  Dependent: Number of Park Attendees

  Function:

  c(a) = 6+29.99a

• Independent: Total Cost

  Dependent: Number of Park Attendees

  Function:

  c(a) = 6a + 29.99a

• Independent: Number of Park Attendees

  Dependent: Total Cost

  Function:

  c(a) = 6+29.99a

• Independent: Total Cost

  Dependent: Number of Park Attendees

  Function:

  c(a) = 6a+29.99

Multiple Choice

The position, p, of the minute hand gives the time, t.

Complete the statement: "___________ is a function of ___________"

• The position of the minute hand is a function of time.

• Time is a function of the position of the minute hand.

Multiple Choice

A bacteria population is 10,000. It triples each day.

Complete the statement: "________ is a function of _________"

• 10,000 is a function of 3.

• 3 is a function of 10,000

• The number of days is a function of bacteria population

• Bacteria population is a population of the number of days

Function Machines
A function machine takes an Input, applies a series of
mathematical operations to it, and then produces a result
as an Output

10

60

55

Multiple Choice

What is the output?

• 19

• 145

• 9

• 8

Multiple Select

Select all possible functions for this function machine

• $$\times3$$  

• $$3$$  

• $$\times2$$  

• $$2$$  

Multiple Choice

Which variable is what changes because of what you manipulated in the experiment?

• Independent

• Dependent

• Constant

• Control

Multiple Choice

What is the input when the output is 2?

• 1

• 4

• 2

• 3

Function Notation

A concise way of substituting specific values for x

Written: f(x)

Read: "f of x"

Multiple Choice

The function h(t) represents the height in inches of a plant after t weeks. What does the notation 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

Think of a function like a machine ...

• Substitute "in" value for x (or other variable)

• Calculate "out" value using Order of Operations

• This example is showing f(x)=5x + 1

• This is read f (of x) = 5x plus 1

• So, with function notation, the y is replaced with f(x).

Draw

If f(x) = 2x² + 5x - 3, evaluate f(-1).

Draw

f(x)=2x+2

Find x when, f(x)= 2

Multiple Choice

• -2

• 24

• 10

• 2

Evaluate from Graphs

• Are you finding x or y?

• If it's f(#) you are finding y and know what x is

• If it's f(x) = # you are finding x and know what y is

Fill in the Blanks

Multiple Select

Given the graph of g(x), evaluate: g(x) = 0.

Select all that apply.

• -5

• -4

• 2

• 3

• 6

Distance - Time Graphs

• Linear (straight) line shows moving at a CONSTANT Rate.

• Non-linear (curved) show acceleration or deceleration.

Multiple Choice

I began to walk; then, I increased my pace and held it constant for a period of time and then decreased my pace slowly. Which graph models this situation?

• A

• B

• C

• D

Multiple Choice

The graph shows how far Jim has traveled since he left his house. How long did Jim have to stop at a light for?

• 2 miles

• 2 minutes

• 5 minutes

• 5 miles

Multiple Choice

The graph represents Kara's trip. Which statement is true?

• Between 10 and 20 minutes Kara's car was stopped

• Kara's highest speed was between 30 and 35 minutes.

• Kara's highest speed was between 25 and 30 minutes.

• Between 5 and 10 minutes Kara's speed was decreasing.

Multiple Select

• f(0)>g(0)

• There are two values of x where f(x)=g(x).

• f(-3)>g(4)