Functions

Functions

Today's Objective: 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!

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

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

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)

Linear Functions

Write an equation in slope intercept form for each representation.

Linear Functions

Write an equation in slope intercept form for each representation.

Remember...

1.) Find the slope

2.) Find the y-intercept (b)

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

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.

• $$y\ =\ -\frac{2}{4}x\ +\ 8$$  

• $$y\ =\ \frac{2}{4}x\ +\ 8$$  

• $$y\ =\ 8x\ +\ \frac{2}{4}$$  

• $$y\ =\ -\frac{4}{2}x\ +\ 8$$  

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

Writing a linear equation with a point and parallel line.

(1) Given y₁=m₁x₁ +b₁ and y2=m₂x₂ +b₂

(2) Identify slope of original line

(3) Substitute slope (m2) and point into the y=mx+b equation.

(4) Parallel Lines: m₂ =m₁

(5) Solve for b.

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