Algebra II Final Review (Aurora Central Catholic)

7.1-7.2

100

For y=2^x, make a table of values.

x: -2 -1 0 1 2 

y: 1/4 1/2 1 2 4 

200

Identify a and b for y=12(0.95)^x

a=12, b=.95

300

You have invested $1000 in savings at the end of 6th grade. It pays 5% annual interest. After 6 years, how much will be in the account?

$1,340.10

400

Find the value of e⁸ and e³.

e⁸=2980.957; e³=20.086

500

Make a table of values for y=2^(x-4)

x= -2 -1 0 1 2 

y=1/64 1/32 1/16 1/8 1/4

7.3

100

What is the log form of 100=10^2?

log₁₀100=2

200

What is the value of log₅125?

x=3

300

What is the common logarithm?

logx=log₁₀^x

400

For y=log₄x, what is the domain, range, y-intercept, and the asymptote.

D: x>0 R: All real numbers

Y-Intercept: N/A Asymptote: x=0

500

For y=alog_b(x-c)+d, wat is a, c, and d?

a: vertical stretch/compression

c: horizontal shift

d: vertical shift

7.4

100

What is the product property?

logbmn=log_bm=log_bn

200

What is the quotient property?

logb(m/n)=log_bm-log_bn

300

What is the power property?

log_bmⁿ=nlog_b^m

400

What is log₄5x+log₄3x as a single logarithm?

log₄(15x²)

500

What is log 4x/y expanded?

log4+logx-logy

7.5

100

Define exponential equation.

Any equation where the exponent includes a variable. 

200

What is the solution to 16^3x=8?

x= 1/4

300

What are the three methods to solve a logarithmic function?

1: Use exponents

2: By graphing

3: Use tables

400

What is the solution to log₁₀(3-2x)=-1?

x=1.45

500

Convert 15^3x=285 into logarithmic form.

log₁₅285=3x

7.6

100

Definition of the natural logarithmic function.

If y=e^x, then x=log_ey=lny=lny

200

What is ln7+2ln5 as a single natural logarithm?

ln175

300

What is 3lnx+2lny+1n5 as a single natural logarithm?

ln5x³y²

400

Solve 4e^2x+2=16.

about .626

500

Solve ln2x+ln3=2

e²=6x