Free Printable Graphing Logs Quiz Review

1.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

2.

Without technology, determine which of the following is an increasing function. Check all that apply.

a)

y = log₂ (x - 4)

b)

y = log₃ (x+3)

c)

y = -2log₅ (x-1)

d)

y = ¹/₂log x + 4

3.

Which of the following has a domain of $\left(2,\ \infty\right)$ ?

a)

y = log₂ x

b)

y = log₃ (x+2)

c)

y = log₄ (x - 2)

d)

y = log₇x - 2

4.

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

a)

b)

c)

d)

5.

Which of the following are not allowed bases, b, in a logarithm? log_b A = P Check all that you believe aren't allowed.

a)

1

b)

0

c)

fractions

d)

decimals

e)

whole numbers

6.

Classify the following graph.

(If you move your mouse over the graph, the image will pop up larger.)

a)

Exponential Growth

b)

Exponential Decay

c)

Logarithmic Growth

d)

Logarithmic Decay

7.

$f\left(x\right)=\log_4x$ Identify ALL of the true characteristics about the function. (There are multiple correct statements!)

a)

As the x-values increase, the values of the function decrease.

b)

As the x-values increase, the values of the function increase.

c)

The x-intercept is (1,0).

d)

The x-intercept is (4,0).

e)

There is no y-intercept.

8.

What is the equation of the asymptote on the graph of $y=\log_5\left(x+3\right)+5$ ?

a)

x = -3

b)

x=5

c)

y= -3

d)

y=5

9.

Compared to the graph of $y=\log_2x$ , the asymptote of $y=\log_2x+1$ will translate...

a)

right one to x = 1

b)

left one to x = -1

c)

no observable translation, and will remain x = 0

10.

Which of the following has a vertical asymptote at $x=4$

a)

$y=2^x-4$

b)

$y=\log_2\left(x-4\right)$

c)

$y=2^x+4$

d)

$y=\log_2\left(x+4\right)$

11.

Select the function with a domain of $\left(-\ \infty,-1\right)$ .

a)

$y=\log_2\left(x+1\right)$

b)

$y=\log_2\left(x-1\right)$

c)

$y=\log_2\left(-x+1\right)$

d)

$y=\log_2\left(-x-1\right)$

12.

What are the coordinates of the x-intercept of y=log₇(x-2)?

a)

(3, 0)

b)

(-2, 0)

c)

(2, 0)

d)

(1, 0)

13.

What is the domain of log(x)?

a)

(-∞, ∞)

b)

[0, ∞)

c)

(0, ∞)

d)

Pickle

14.

What is the range of log(x)?

a)

(-2, 4)

b)

(-∞, ∞)

c)

(-∞, 0)

d)

Cucumber

15.

Classify the following graph.

a)

Exponential Growth

b)

Exponential Decay

c)

Logarithmic Growth

d)

Logarithmic Decay

16.

Classify the following graph.

a)

Exponential Growth

b)

Exponential Decay

c)

Logarithmic Decay

d)

Logarithmic Growth

17.

Classify the following graph.

a)

Exponential Growth

b)

Exponential Decay

c)

Logarithmic Decay

d)

Logarithmic Growth

18.

What equation matches the graph?

a)

f(x) = 3^x

b)

f(x) = (⅓)^x

c)

f(x) = log₃(x)

d)

$\log_{\frac{1}{3}}\left(x\right)$

19.

Which has a horizontal asymptote?

a)

Exponential

b)

Logarithmic

c)

Both

20.

Which has a vertical asymptote?

a)

Exponential

b)

Logarithmic

c)

Both

21.

Where is the asymptote?

a)

x = 1

b)

y = 1

c)

x = -1

d)

y = -1

22.

As x --> 1, f(x) --> ____

a)

0

b)

∞

c)

-∞

d)

1

23.

As x --> ∞, f(x) --> ____

a)

0

b)

∞

c)

-∞

d)

1

24.

Describe the transformation of y=ln(x) that would give the graph for y = ln(-x)

a)

reflection over the line y=x

b)

reflection over the x-axis

c)

reflection over the y-axis

d)

reflection over the line y=-1

25.

Describe the transformation of y=ln(x) that would give the graph for y = 7ln(x)

a)

vertical translation 7 up

b)

vertical stretch by a factor of 7

c)

vertical compression by a factor of 7

d)

horizontal translation 7 left

26.

Which of the following transformations would take f(x)= lnx to g(x)= −ln(x+5)

a)

reflection over the x-axis

b)

reflection over the y-axis

c)

translate right 5

d)

translate up 5

e)

translate left 5

27.

Match the graph with its equation

a)

y = log₄ (x)+2

b)

y = log₄ (x + 2) + 1

c)

y = log₄ (x - 1) + 2

d)

y = log₄ (-x + 2)

28.

Domain of y = log x ?

a)

(-∞, ∞)

b)

(0, ∞)

c)

[0, ∞)

d)

[-∞, ∞]

29.

What is the correct transformed equation for the graph?

a)

y = log(x - 4)

b)

y = log(x) - 4

c)

y = log(x + 4)

d)

y = log(x) + 4

30.

Which graph best represents the following logarithmic function?
$y=\log_4x$

a)

b)

c)

d)

31.

Find the domain and range of:
f(x) = ln(x)

a)

D: all real numbers
R: y > 0

b)

Domain: all real numbers
Range: all real numbers

c)

Domain: x > 0
Range: all real numbers

d)

Domain: all real numbers
Range: y < 0

32.

What is the rate of change (-2,6) and (1,1)?

a)

$\frac{5}{3}$

b)

$-\frac{5}{3}$

c)

$\frac{3}{5}$

d)

$-\frac{3}{5}$

33.

Find the rate of change of Pete's height from 3 to 5 years.

a)

8

b)

2

c)

4

d)

$\frac{2}{8}$

34.

What is the formula for rate of change?

a)

y₂-y₁ / x₂-x₁

b)

x₂-x₁ / y₂-y₁

35.

Find the average rate of change over the given interval.

a)

4

b)

7

c)

7/3

d)

3/7

36.

Find the average rate of change over the given interval.

a)

3

b)

1.5

c)

1

d)

0.67

37.

Find the average rate of change over the given interval.

a)

-2

b)

2

c)

-1

d)

-0.5

38.

Find the average rate of change over the given interval.

a)

3

b)

1.5

c)

1

d)

0.67

39.

Find the average rate of change of f(x)= $2\log_2x+5$ from 1 to 2.

a)

1

b)

1/2

c)

2

d)

-2

40.

What is the base and x-intercept in the equation of the graph: $y\ =\ \log_3x$

a)

Base is 3; x-intercept: (1, 0)

b)

Base is 3; x-intercept is (0, 1)

c)

Base is 1; x intercept: (0, 3)

d)

Base is 1; x-intercept is (3, 0)

41.

f(x)=log₅(x+4) - 2

Describe the asymptote

a)

Horizontal Asymptote x = -4

b)

Vertical Asymptote x = -4

c)

Horizontal Asymptote x = 4

d)

Vertical Asymptote x = 4

42.

f(x)=2ln(x+2)

Describe the transformation

a)

Vertical Stretch by 2, translation 2 units to the left

b)

Vertical Compression by 2, translation 2 units to the left

c)

Vertical Stretch by 2, translation 2 units to the right

d)

Vertical Compression by 2, translation 2 units to the right

Graphing Logs Quiz Review

Total questions: 42

Worksheet time: 2hrs 47mins

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