RELATION FUNCTIONS

Functions

Today's Objective: I can determine if a relation is a function

When you put an input into a machine you can only get out one input.

THAT'S A FUNCTION!

(Each input has only one output)

These are all functions

EACH X VALUE

HAS ONLY ONE Y VALUE

These are NOT functions

In each example

there is an X VALUE that has more than one Y VALUE

Multiple Choice

Is the relation a function? Why.

• Yes, because the x-value 11 has two y-values paired 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 paired with it.

• No, because each x-value has only one y-value paired with it.

Multiple Choice

Is this table a function or not a function?

• Function

• Not a Function

Multiple Choice

Is this mapping a function or not a function?

• Function

• Not a Function

Remember, in order to be a function, x cannot repeat

• In tables or ordered pairs, just check the domain (the x values)

• With mapping, each input can go to only one output

• With graphs, use the vertical line test to see if any vertical lines touch the function more than once (which would mean x repeated)

Multiple Choice

Is this set of ordered pairs a function or not a function?

• Function

• Not a Function

Multiple Choice

Is this set of ordered pairs a function or not a function?

• Function

• Not a Function

The vertical line test

• To tell if a graph is a function, draw a vertical line anywhere on the graph.

• If any vertical line touches the graph in more than one location it is NOT a function

Multiple Choice

Which graph does NOT pass the vertical line test?

• Graph 1

• Graph 2

• Graph 3

• Graph 4

Multiple Choice

Is this graph 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

Is this graph 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

Is this graph a function or not a function?

• Function

• Not a Function

Remember, to evaluate functions, substitute the given value in for x.

• For example, if f(x) = 4x - 8, then f(3) = 4(3) - 8, which means f(3) = 4

Multiple Choice

f(x)=x²-5x
f(4)=

• -4
• 126
• 24
• 84

Multiple Choice

f(x) = 3x² - 11
Find f(-5)

• f(-5) = 64
• f(-5) = -86
• f(-5) = 214
• f(-5) = -7

Multiple Choice

Evaluate f(t)=-2t²+ 1 for f(-3)

• 19
  
• 37
• -17
• -11

Multiple Choice

g(x) = 11 - x
Find g(x) = -7 

• 4
• 17
• 18
• -77

1.) Find the slope

2.) Find the y-intercept (b)

3.) Plug both values into y = mx + b

Slope-intercept Form

Multiple Choice

Write an equation in slope-intercept form:

$$slope\ =\ -\frac{2}{3}$$   $$y-intercept\ =\ \left(0,\ -9\right)$$  

• $$y\ =\ -\frac{2}{3}x\ +\ 9$$  

• $$y\ =\ -\frac{2}{3}x\ -\ 9$$  

• $$y\ =\ -9x\ +\ \frac{2}{3}$$  

• $$y\ =\ -9x\ -\ \frac{2}{3}$$  

Multiple Choice

Write an equation in slope-intercept form:

$$Slope\ =\ 10$$  

$$y-intercept\ =\ \left(0,\ 8\right)$$  

• $$y\ =\ 8x\ -\ 10$$  

• $$y\ =\ 8x\ +\ 10$$  

• $$y\ =\ 10x\ -\ 8$$  

• $$y\ =\ 10x\ +\ 8$$  

Multiple Choice

Write an equation in slope-intercept form:

$$Slope\ =\ \frac{3}{8}$$  

$$y-intercept\ =\ \left(0,\ -1\right)$$  

• $$y\ =\ \frac{3}{8}x\ -\ 1$$  

• $$y\ =\ \frac{3}{8}x\ +\ 1$$  

• $$y\ =\ 1x\ +\ \frac{3}{8}$$  

• $$y\ =\ 1x\ -\ \frac{3}{8}$$  

From a Graph

Find the Slope

Find the y-intercept

Plug in the values to y = mx + b

Multiple Choice

Write an equation for the graph shown.

• $$y\ =\ -\frac{3}{1}x\ +\ 2$$  

• $$y\ =\ \frac{1}{3}x\ +\ 2$$  

• $$y\ =\ \frac{3}{1}x\ +\ 2$$  

• $$y\ =\ 2x\ +\ \frac{3}{1}$$  

Multiple Choice

Write the equation for the graph shown.

• $$y\ =\ \frac{2}{1}x\ +\ 9$$  

• $$y\ =\ -\frac{1}{2}x\ -\ 9$$  

• $$y\ =\ -\frac{2}{1}x\ +\ 9$$  

• $$y\ =\ \frac{1}{2}x\ +\ 9$$  

Multiple Choice

Write the equation for the graph shown.

• $$y\ =\ -\frac{2}{4}x\ +\ 8$$  

• $$y\ =\ \frac{2}{4}x\ +\ 8$$  

• $$y\ =\ 8x\ +\ \frac{2}{4}$$  

• $$y\ =\ -\frac{4}{2}x\ +\ 8$$  

From a Table

Find the slope

Find the y-intercept

Plug the values into y = mx + b

Multiple Choice

Write the equation that represents this table.

• y = 6 - 4x

• y = -4 + 6x

• y = -6 + 4x

• y = -2 + 3x

Multiple Choice

Write an equation for the table shown.

• $$y\ =\ 3x\ +\ 4$$

• $$y\ =\ 3x\ -\ 2$$

• $$y\ =\ \frac{1}{3}x\ +\ 4$$

• $$y\ =\ -3x\ +\ 4$$  

Multiple Choice

Write the equation that represents this table.

• y = 5 + 3x

• y = 5 + 2x

• y = -2 + 5x

• y = 5 - 3x

Multiple Choice

Write an equation for the table shown.

• $$y\ =\ \frac{1}{3}x\ +\ 6$$

• $$y\ =\ \frac{1}{3}x\ -\ 2$$

• $$y\ =\ -2x\ +\ \frac{1}{3}$$

• $$y\ =\ \frac{3}{1}x\ -\ 2$$

Multiple Choice

Write an equation for the table shown.

• $$y\ =\ \frac{1}{3}x\ +\ 6$$

• $$y\ =\ \frac{1}{3}x\ -\ 2$$

• $$y\ =\ -2x\ +\ \frac{1}{3}$$

• $$y\ =\ \frac{3}{1}x\ -\ 2$$

Multiple Choice

Gil has $200 saved for snacks. He will spend $5 on snack per week until he runs out.

• $$y\ =\ 200-5x\$$

• $$y\ =\ 5x\ +\ 200$$

• $$y\ =\ -200x\ +\ 5$$

Multiple Choice

The local service center advertises that it charges a flat fee of $50 plus $8 per mile to tow a vehicle. Write an equation that represents the total cost (C) of a service for m miles of towing.

• y = 8x + 50

• C = 50m +8

• y = 50x + 8

• C = 8m + 50

Multiple Choice

The amusement park charges $20 to get in plus $1.50 per ride. Which linear equation below represents this relationship.

• y=1.5+20x

• y=1.5x + 20

• y = 20x + 1.5

• y= 21.5x