Is it a function? & Function Notation

Is it a function? &
Function Notation

By Katie Yingling

How do I know if it's a function?

The "x" cannot repeat!

Each number for x can only be used one time because each input, x, can only have one output, y.

we use the Vertical Line Test to determine if it's a function. The vertical line can only touch the graph once.

On the graph

each number for x can only be used one time. X cannot repeat. Y doesn't matter.

​​On a table

each number for x can only match with one number for y. In this case, the inputs, x, have more than one output, y.

​​In a map

each number for x can only be used once. X cannot repeat. Y doesn't matter.

​​In a set

Multiple Choice

Which set of values is a function?

• (9,5) (10,5) (9,-5) (10,-5)
• (3,4) (4,-3) (7,4) (3, 8)
• (6,-5) (7, -3) (8, -1) (9, 1)
• (2, -2) (5, 9) (5, -7) (1, 4)

Multiple Choice

Is this mapping a function or not a function? 

• Function
• Not a Function

Multiple Choice

Is this table a function or not a function? 

• Function
• Not a Function

Multiple Choice

Is this graph a function or not a function? 

• Function 
• Not a Function

Multiple Choice

• Function
• Not a Function

Multiple Choice

Which graph does NOT pass the vertical line test?

• Graph 1
• Graph 2
• Graph 3
• Graph 4

Multiple Choice

.

• Function
• Not a Function

Multiple Choice

What is the definition of function?

• Has inputs and outputs
• Every input has only ONE output
• Inputs have different outputs every time
• x-values and y-values

Function Notation

Writing an equation with f(x)= instead of y=

Sometimes it's better to write an equation in function notation to represent different values of x and y that are solutions to the equation.

​Function Notation:

​Function Notation:

With f(x), since x is in the parentheses, plug in the number in parentheses for x and find the y value. Therefore, when x is 4, y is 11.

​Function Notation:

Multiple Choice

$$f\left(x\right)$$  

is the same thing as ______.

• y

• x

• input

• an equation

Multiple Choice

How would you write

$$y=2x-3$$  in function notation?

• $$y=2x-3$$  
  

• $$f=2x-3$$  

• $$f\left(x\right)=2x-3$$  
  

Multiple Choice

How do you read 

$$f\left(x\right)$$  ?

• f x

• f of x

• f parenthesis x

• f with an x inside parenthesis

Multiple Choice

Translate the function notation into a coordinate point.

$$f\left(-1\right)=5$$  

• $$\left(-1,5\right)$$  

• $$\left(1,5\right)$$  

• $$\left(5,1\right)$$  

• $$\left(5,-1\right)$$  

Multiple Choice

Translate the coordinate pair into function notation.

$$\left(0,8\right)$$  

• $$f\left(0\right)=8$$  

• $$f\left(0\right)=-8$$  

• $$f\left(8\right)=0$$  

• $$f\left(-8\right)=0$$  

Multiple Choice

Given the function
$$f\left(x\right)=x+3$$  

Evaluate: 

$$f\left(-2\right)$$  

• $$f\left(-2\right)=-1$$  

• $$f\left(-2\right)=1$$  

• $$f\left(-2\right)=5$$  
  

• $$f\left(-2\right)=-5$$  
  

Multiple Choice

Given 
  $$g\left(x\right)=4x-2$$  

Evaluate: 

$$g\left(-7\right)$$  

• $$g\left(-7\right)=-30$$  

• $$g\left(-7\right)=-26$$  

• $$g\left(-7\right)=-36$$  

• $$g\left(-7\right)=26$$  

Multiple Choice

Given:
$$f\left(x\right)=6x$$  

Find x when  $$f\left(x\right)=-24$$  

• $$x=-4$$  

• $$x=4$$  

• $$x=-144$$  

• $$x=-6$$  

Multiple Choice

Given:
$$g\left(x\right)=3x-5$$  

Find x when  $$g\left(x\right)=4$$  

• $$x=3$$  

• $$x=-3$$  

• $$x=7$$  

• $$x=-3$$  

Multiple Choice

Given the graph, 

find:

$$f\left(2\right)$$  

• $$f\left(2\right)=5$$  

• $$f\left(2\right)=4$$  
  

• $$f\left(2\right)=3$$  
  

• $$f\left(2\right)=0$$  
  

Multiple Choice

Given the graph, 

find:

$$f\left(4\right)$$  

• $$f\left(4\right)=3$$  

• $$f\left(4\right)=1$$  
  

• $$f\left(4\right)=2$$  
  

• $$f\left(4\right)=0$$  
  

Multiple Choice

Given the graph, 

find the value of x when: 

$$f\left(x\right)=0$$  

• $$x=1$$  

• $$x=0$$  
  

• $$x=7$$  
  

• $$x=2$$  
  

Multiple Choice

Given the graph, 

find the value of x when: 

$$f\left(x\right)=5$$  

• $$x=5$$  

• $$x=0$$  
  

• $$x=3$$  
  

• $$x=2$$