RELATION FUNCTIONS

RELATION FUNCTIONS

Presentation

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Hard

Created by

Ibu K

FREE Resource

11 Slides • 29 Questions

1

Functions

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

2

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)

3

4

These are all functions

EACH X VALUE

HAS ONLY ONE Y VALUE

5

These are NOT functions

In each example

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

6

Multiple Choice

Question image

Is the relation a function? Why.

1

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

2

Yes, because each x-value has only one y-value paired with it.

3

No, because the x-value 11 has two y-values paired with it.

4

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

7

Multiple Choice

Question image

Is this table a function or not a function?

1

Function

2

Not a Function

8

Multiple Choice

Question image

Is this mapping a function or not a function?

1

Function

2

Not a Function

9

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)

10

Multiple Choice

Question image

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

1

Function

2

Not a Function

11

Multiple Choice

Question image

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

1

Function

2

Not a Function

12

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

13

Multiple Choice

Question image

Which graph does NOT pass the vertical line test?

1

Graph 1

2

Graph 2

3

Graph 3

4

Graph 4

14

Multiple Choice

Question image

Is this graph a function or not a function?

1

Function

2

Not a Function

15

Multiple Choice

Question image

Is this graph a function or not a function?

1

Function

2

Not a Function

16

Multiple Choice

Question image

Is this graph a function or not a function?

1

Function

2

Not a Function

17

Multiple Choice

Question image

Is this graph a function or not a function?

1

Function

2

Not a Function

18

Multiple Choice

Question image

Is this graph a function or not a function?

1

Function

2

Not a Function

19

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

20

Multiple Choice

f(x)=x²-5x
f(4)=

1

-4

2

126

3

24

4

84

21

Multiple Choice

f(x) = 3x² - 11
Find f(-5)

1

f(-5) = 64

2

f(-5) = -86

3

f(-5) = 214

4

f(-5) = -7

22

Multiple Choice

Evaluate f(t)=-2t²+ 1 for f(-3)

1

19

2

37

3

-17

4

-11

23

Multiple Choice

g(x) = 11 - x
Find g(x) = -7

1

4

2

17

3

18

4

-77

24

1.) Find the slope

2.) Find the y-intercept (b)

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

Slope-intercept Form

25

Multiple Choice

Write an equation in slope-intercept form:

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

1

$y\ =\ -\frac{2}{3}x\ +\ 9$

2

$y\ =\ -\frac{2}{3}x\ -\ 9$

3

$y\ =\ -9x\ +\ \frac{2}{3}$

4

$y\ =\ -9x\ -\ \frac{2}{3}$

26

Multiple Choice

Write an equation in slope-intercept form:

$Slope\ =\ 10$

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

1

$y\ =\ 8x\ -\ 10$

2

$y\ =\ 8x\ +\ 10$

3

$y\ =\ 10x\ -\ 8$

4

$y\ =\ 10x\ +\ 8$

27

Multiple Choice

Write an equation in slope-intercept form:

$Slope\ =\ \frac{3}{8}$

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

1

$y\ =\ \frac{3}{8}x\ -\ 1$

2

$y\ =\ \frac{3}{8}x\ +\ 1$

3

$y\ =\ 1x\ +\ \frac{3}{8}$

4

$y\ =\ 1x\ -\ \frac{3}{8}$

28

From a Graph

Find the Slope

Find the y-intercept

Plug in the values to y = mx + b

29

Multiple Choice

Question image

Write an equation for the graph shown.

1

$y\ =\ -\frac{3}{1}x\ +\ 2$

2

$y\ =\ \frac{1}{3}x\ +\ 2$

3

$y\ =\ \frac{3}{1}x\ +\ 2$

4

$y\ =\ 2x\ +\ \frac{3}{1}$

30

Multiple Choice

Question image

Write the equation for the graph shown.

1

$y\ =\ \frac{2}{1}x\ +\ 9$

2

$y\ =\ -\frac{1}{2}x\ -\ 9$

3

$y\ =\ -\frac{2}{1}x\ +\ 9$

4

$y\ =\ \frac{1}{2}x\ +\ 9$

31

Multiple Choice

Question image

Write the equation for the graph shown.

1

$y\ =\ -\frac{2}{4}x\ +\ 8$

2

$y\ =\ \frac{2}{4}x\ +\ 8$

3

$y\ =\ 8x\ +\ \frac{2}{4}$

4

$y\ =\ -\frac{4}{2}x\ +\ 8$

32

From a Table

Find the slope

Find the y-intercept

Plug the values into y = mx + b

33

Multiple Choice

Question image

Write the equation that represents this table.

1

y = 6 - 4x

2

y = -4 + 6x

3

y = -6 + 4x

4

y = -2 + 3x

34

Multiple Choice

Question image

Write an equation for the table shown.

1

$y\ =\ 3x\ +\ 4$

2

$y\ =\ 3x\ -\ 2$

3

$y\ =\ \frac{1}{3}x\ +\ 4$

4

$y\ =\ -3x\ +\ 4$

35

Multiple Choice

Question image

Write the equation that represents this table.

1

y = 5 + 3x

2

y = 5 + 2x

3

y = -2 + 5x

4

y = 5 - 3x

36

Multiple Choice

Question image

Write an equation for the table shown.

1

$y\ =\ \frac{1}{3}x\ +\ 6$

2

$y\ =\ \frac{1}{3}x\ -\ 2$

3

$y\ =\ -2x\ +\ \frac{1}{3}$

4

$y\ =\ \frac{3}{1}x\ -\ 2$

37

Multiple Choice

Question image

Write an equation for the table shown.

1

$y\ =\ \frac{1}{3}x\ +\ 6$

2

$y\ =\ \frac{1}{3}x\ -\ 2$

3

$y\ =\ -2x\ +\ \frac{1}{3}$

4

$y\ =\ \frac{3}{1}x\ -\ 2$

38

Multiple Choice

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

1

$y\ =\ 200-5x\$

2

$y\ =\ 5x\ +\ 200$

3

$y\ =\ -200x\ +\ 5$

39

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.

1

y = 8x + 50

2

C = 50m +8

3

y = 50x + 8

4

C = 8m + 50

40

Multiple Choice

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

1

y=1.5+20x

2

y=1.5x + 20

3

y = 20x + 1.5

4

y= 21.5x

Functions

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

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