Free Printable Algebra 2 Semester 2 Review

1.

What is the inverse of the function f(x)=3x−6

a)

f^-1(x)=1/3x+2

b)

f^-1(x)=−3x+6

c)

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

d)

f^-1(x)=1/2x+3

2.

Identify the domain and range of the equation:

f\left(x\right)=\frac{1}{x-4}+\ 1

a)

Domain: $x\ne4$ Range: $y\ne1$

b)

Domain: $x\ne4$ Range: $y\ne-1$

c)

Domain: $x\ne-4$ Range: $y=1$

d)

Domain: $x\ne-4$ Range: $y\ne-1$

3.

Simplify and state the excluded values:

\frac{m+8}{m^2+12m+32}

a)

$\frac{1}{m-2};\ m\ne0,2$

b)

$\frac{1}{m+4};\ m\ne-8,-4$

c)

$\frac{1}{m+4};\ m\ne-4$

d)

$\frac{1}{m+8};\ m\ne-8$

4.

Simplify the expression:

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5.

$\frac{3x}{x+4}+\frac{5}{x-6}$

Simplify. Enter your result in the space provided.

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6.

Solve the equation. Remember to check for extraneous solutions:

\frac{1}{2a}=\frac{a+3}{a^2}+\frac{1}{a}

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7.

Sketch the graph of the function.

a)

b)

c)

d)

8.

You take 1,100 mg of an antibiotic with a half-life of 8 hours. How much antibiotic is left in your system after 20 hours?

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9.

You deposit $1,600. in an account that pays 3.1% compounded continuously. Find the balance after 3 years.

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10.

Solve the equation. Round your answer to the nearest ten-thousandth.

a)

9.3838

b)

9.7778

c)

9.7324

d)

9.6543

11.

$\left(\frac{31}{20}\right)^u=v$

Rewrite the equation in logarithmic form.

a)

$\log_v\frac{31}{20}=u$

b)

$\log_u\frac{31}{20}=v$

c)

$\log_{\frac{31}{20}}v=u$

d)

$\log_{\frac{31}{20}}u=v$

12.

$\log_2\frac{1}{8}$

Solve.

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13.

Expand the log:

a)

b)

c)

d)

14.

$10\log_32k=30$

Solve the equation.

a)

$\frac{27}{2}$

b)

$-\frac{9}{2}$

c)

$737$

d)

$8$

15.

What is the point of discontinuity?

a)

x = -3

b)

(-3,2)

c)

x = -5

d)

(3,8)

16.

Which is the graph of the rational equation:

a)

b)

c)

d)

17.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 1

d)

y = 9

18.

What's the vertical asymptote of the function?

a)

x = -9

b)

x = 9

c)

x = 3 , x = -3

d)

x = 3

19.

What's the vertical asymptote of the function?

a)

x = 4

b)

x = 16

c)

x = 4 , x = -4

d)

No vertical asymptote

20.

Who is the last shark mentioned in the song, "Baby Shark"?

a)

Grandma Shark

b)

Grandpa Shark

c)

Mommy Shark

d)

Daddy Shark

Algebra 2 Semester 2 Review

Total questions: 20

Worksheet time: 21mins

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