U2 Function Notation

Understanding Function Notation

Multiple Choice

Find the value of y in the equation $$y=4x-1$$ when $$x=2$$

• 4

• 5

• 7

• 0

Multiple Choice

Write an equation to represent the scenario.

The cost of renting a bike is $10 to take the bike and $4 for every hour it spends in our possession.

• y = 10x + 4

• y = 10 + 4x

• y = 14x

• 4x = 30

Multiple Select

Select all the statements that are true about the graph

Function Notation

What is it?

Function notation is a specific notation used to represent a relationship between an input and an output.

Function Notation

What it looks like

A function can be thought of as a machine that assigns one output to every input.

Let's take a closer look

​Read and analyze the diagram.

Multiple Choice

Find $$f\left(-3\right)$$

• -2

• 1

• 8

• no solution

Multiple Choice

Find $$f\left(-2\right)$$

• f(x) = 9

• f(x) = -9

• f(x) = -15

• f(x) = 21

Dropdown

In the graph f(0) =​ ​

Select answer

Writing Equations in Function Notation

Writing Function Notation

Equations

Writing equations in function notation is very similar to what you have done in the past.

Instead of using y to represent your output in your equations you are now going to use function notation.
For example, instead of y=mx+b it could g(x) = mx+b or f(t)= mt+b

Ordered Pairs

Instead of using y to represent your output in your equations you are now going to use function notation.
For example,
if F(5) = 7 the ordered pair would be (5,7)
if g(-4) = 2 the ordered pair would be (-4,2)

Multiple Choice

C(x) = 400x + 70,000 represents the cost in dollars a company has in manufacturing x items during a month. Based on this, what does c(100) represent?

• It cost $100 to make all the items for the month

• The cost to make 100 items during a month.

Writing Function Notation

Graphs

Multiple Choice

Using f(x) , g(x) , or h(x) instead of y is called using ......

• 
  Slope Notation

• Variable Notation

• Intercept Notation

• Function Notation

Writing Function Notation for Graphs

Examples

Drag and Drop

Write the equation for this graph in function notation.

1. The slope is ​

Placeholder

2.The y-intercept is ​
Placeholder
​

3. The function for this graph would be ​
Placeholder

Drag these tiles and drop them in the correct blank above

3

4

-3

-1.5

Multiple Choice

"You can eat 6 animal crackers per minute.  There are 200 animal crackers in the jar when you started eating."

Write a function to represent the number of animal crackers left in the jar after x minutes.

HINT - EATING IN THIS CONTEXT MEANS THE NUMBER OF ANIMAL CRACKERS IS DECREASING

• 
  f(x) = 200x + 6

• f(x) = −200x + 6

• 
  f(x) = −6x + 200

• 
  f(x) = 6x + 200

Multiple Choice

For babysitting, Nicole charges a flat fee of $3, plus $5 per hour. Write an equation in function notation to represent this situation, where the total amount she earns would be represented by m(x).

• $$m\left(x\right)=3x+5$$

• $$m\left(x\right)=5x+3$$

• $$m\left(x\right)=8x$$

• $$m\left(x\right)=5x-3$$