Final Exam Review: Functions

Inverses

100

Find the inverse

f(x) = x - 3

x + 3

200

find the inverse

f(x) = log₄(x+1)

4^x - 1

300

Find f^-1(3)

f(x) = (5x)/(x-1)

-3/2  

400

find f^-1(8) when f(x) = e^x-3

^{Round 3 sig figs}

5.08

500

Find f^-1(x) when f(x) = 3ln(x)

e^x/3

Intercepts

100

Find the x-intercept

y = 8x + 5

x = -5/8 = -0.625

200

Find the y-intercept

y = 2(x + 1)² - 3

-1

300

Find the x-intercept. Round 3 sig figs.

y = log₃(x - 1) + 2

x = 1.11

400

Find the y-intercept. Round 3 sig figs.

y = 5e^x+2

36.9

500

Find the x-intercepts.

y = -6x² - 3x + 9

there are no x-intercepts

Domain

100

What is the domain?

y = 3x + 5

x e R

200

what is the domain?

y = 4^x + 5

x e R

300

Find the domain

y = log(4x + 8)

x > -2

400

Find the domain.

y = 1 / (x+1)

x e R, except x cannot be -1

500

Find the domain.

y = ln(2x - 3)

x > 3/2

Range

100

What is the range of y = 5^x

y > 0

200

What is the range of y = log(x)

y e R

300

What is the range?

y = x² + 8

y is greater than or equal to 8

400

What is the range?

y = 4^x - 9

y > -9

500

What is the range?

y = x² - 4x + 4

y is greater than or equal to 0

Transformations

100

Describe the transformation

f (x) + 4

up 4

200

Describe the transformation

f(x + 8)

left 8

300

Describe the transformation

-f(x)

reflection about x-axis

400

Describe the transformations

f(x - 4) + 1

right 4 and up 1

500

Describe the transformations

f(-x) + 5

reflection about y-axis and up 5