Algebra 2 Review

5.7 Functional Composition

100

What is the domain and range of 

f: 2x+5

g: x-3

What is all real numbers.

200

Solve 

f: 3x+3

g: x²

f(g(x))

3x²+3

300

Solve

f:2x+5

g:root x-3

f(g(x))

2(roots x-3)+5

400

Solve 

f:x²+1

g: 2x-2

g(f(x))

4x²-8x+5

500

Solve 

f:x^2.         

g: x-4    

f(g(4))     

f(g(4))= 0

5.8 Inverse Functions

100

What are the steps to solve an inverse function?

1. switch the x and y

2. solve normally for y

200

What is an easy way to tell on a graph if the equation is invertible?

What is the horizontal line test?

300

Solve

f(x)=2x

f^-1(x)= x/2

400

Solve

f(x)=-x+16

f^-1(x)= -x+16

500

Solve 

f(x)=1/3x-2

f^-1(x)= 3x+6

6.1 Exponential Growth & Decay

100

What is the growth factor of

24,763(1+0.035)² 

1.035

200

How many times does this compound?

5000(1+0.05/365)^365x3

It compounds daily for 3 years

300

Your friend invests $1,500 in a bank account that earns 4% interest compounded quarterly. How much money will be in the account after 8 years?

$2,062.41

400

A student deposits $2,000 into a college fund that earns 5% annual interest compounded annually. How much money will be in the account at the end of the 6 years?

$2,680.19

500

You deposit $3 million into a savings account that earns 0.6% interest compounded monthly. The money stays in the account for 5 years. How much money did you make after 5 years?

You make $91,350

6.2 Natural Base

100

Solve 

e⁵ x e²=

e⁷

200

Solve

49e⁵ / 7e⁴ =

7e

300

Solve 

(10e^-3x)³

1000e^-9x

400

Solve 

root 64e^2x

8e^x

500

What is the value of the symbol e (at least 2 decimal places)?

2.718

6.3 Logarithms

100

What is the change of base formula?

log_ba 

log a / log b

200

What form is this question in?

log₇ 343=3

What is log form.

300

3⁴=81

log₃ 81=4

400

log_1/3 27=-3

1/3^-3=27

500

ln(x−2)=4

x=e⁴+2