Functions Review

Functions

100

Every input has one output

What is a function?

200

Is this a function?

{(1, 2), (1, 3), (1, 4), (1, 5)}

No

300

Is a vertical line a function?

No

400

Is this a function? 

{(1, 2), (2, 2), (3, 2), (4, 2)}

Yes

500

Is a circle a function?

No! 

Linear Functions

100

An equation where the slope is a constant rate of change

Linear!

200

Is y=2x² + 3 a linear function?

No-no power for x!

300

Is y=3x-7 a linear function? 

Yes! 

400

Do the points below make a linear function?

{(0, 4), (2, 8), (3, 10)}

Yes! Y-intercept of 4, slope of 4: y=4x+4

500

Is this a linear function? A y-intercept of (0, 27) and each step to the right multiplies by 1/2

No, linear functions only add or subtract each step!

Writing Equation

100

Y-intercept (0, -3)

Slope: 2

y=2x-3

200

Y-intercept: 4

Slope: -1/2

y= -1/2x + 4

300

Y-intercept: -2

Slope: 2

y= 2x - 2

400

Write the rule:

(0, 5), (1, 8)

y=3x+5

500

Write the rule:

(-1, -4), (1, 10)

y=7x + 3

Substitution

100

What is f(2) when f(x)=4x-6?

f(2) = 4(2) - 6

=8-6

=2

200

What is f(4) for f(x)=5x-7

f(4)=13

300

What is x when y=10?

y=2x-4

10=2x-4 --> x=7

add 4 to both sides

14=2x

divide by 2

x=7

400

What is y when x=8? 

y=1/2x+3

y=7

500

What is x when y=4?

Y=2x+10

-3

Graphs

100

Find the point for x=0:

y=2x-9

(0, -9)

200

What is the y-intercept and slope for:

y=-2x+7

y-intercept: (0, 7)

slope: -2

300

What is the y-intercept and slope for 

2x+y=8

y-intercept: (0, 8)

slope= -2

400

What is the slope for 2y=6x-5

slope = 3

500

What is the y-intercept of 2x+3y=12?

(hint: get into y=mx+b)

(0, 4)