Free Printable Alg2 Unit 6 Test - Exp & Log Functions

Worksheets

Alg2 Unit 6 Test - Exp & Log Functions

Total questions: 23

Worksheet time: 36mins

Name

Class

Date

Find the domain and range of the function whose graph is shown.

D = {x | x > 0}; R = {y | y > 0}

D = {x | all real numbers}; R = {y | y > 0}

D = {x | x > 0}; R = {all real numbers}

D = {all real numbers}; R = {y | y < 0}

none of these are correct (something is wrong in one part or both)

Which function represents exponential growth?

y = (9/5)^x

y = 4x^4

y = 12(1/5)^x

y = 10(3)^x

Solve 8^x+2 = 32^{2x + 4}.

(a)

Solve 2^3m-4 > 4.

m | m < 0

m | m > 0

m | m > 2

m | m > 5/3

no solution; you can't solve exponential inequalities

Write the equation 4³ = 64 in logarithmic form.

Write the equation log₁₂ 144 = 2 in exponential form.

Evaluate log₂ 8.

(a)

Solve log₃ n = 2.

(a)

Solve log₂ 2m > log₂ (m + 5).

(a)

10.

Approximate the value of log₅4 to the nearest thousandth

(a)

11.

Solve 4^x = 20. Round to the nearest ten-thousandth.

(a)

12.

Solve 3^x > 21. Round to the nearest ten-thousandth.

F) {x | x > 0.8451}

G) {x | x > 2.7712}

H) {x | x > 3.0608}

J) {x | x > 7.0000}

13.

Express log₉ 22 in terms of common logarithms.

14.

Which of the following is the sketch of the graph of y = -log₃ (x+5) ?

15.

3^{2x – 6} = 81

(a)

16.

log₃(x-3) + 10 = 14

(a)

17.

Given the original exponential function defined by y=4^x, how would the graph change if the function were:

y=2(4)^x-3+1?

Vertically stretched by a factor of 2, right 3, and up 1

Vertically compressed by a factor of 1/2, left 3 and down 1

Vertically compressed by a factor of 1/2, right 3, and down 1

Vertically stretched by a factor of 2, left 3, and up 1

18.

For $y=a\left(b\right)^x+k$ , how does adding a constant "k" transform the parent function?

Horizontal shift

Vertical Translation

Reflection over the x-axis

Reflection over the y-axis

19.

State the following for the equation $h\left(x\right)=2\cdot4^{\left(x+6\right)}+7$

Horizontal Asymptote: (a)

Domain: (b)

Range: (c)

Choose from the below words

y = 7

$\left(-\infty,\infty\right)$

$\left(7,\infty\right)$

x=7

$\left(-6,\infty\right)$

$\left(-\infty,7\right)$

$\left(7,-\infty\right)$

20.

If f(x) = 2e^x , then what is the f(0)?

(a)

21.

log₄(3x-1)=log₄(2x+3)

(a)

22.

Mrs. Cruise isn't sure if she solved this logarithmic equation correctly. Check her work to determine if she made any mistakes. If she did make a mistake, determine what it was.

She did not convert to exponential form correctly.

She should have divided the arguments.

She used the incorrect base when converting to exponential form.

No mistakes were made!

23.

Solving Exponential Equations Using Logarithms:

Solve for x

$4^x-5=12$

0.489

2.552

0.893

2.044

100 %

Alg2 Unit 6 Test - Exp & Log Functions

Total questions: 23

Worksheet time: 36mins

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