Free Printable Unit 6b Test Review

1.

Logarithms are the inverse of ___________.

a)

Trees

b)

Quadratics

c)

Square

d)

Exponential

2.

Find the inverse of f(x)=log₅x

a)

f^-1(x)=log_x5

b)

f^-1(x)=x⁵

c)

f^-1(x)=5^x

d)

f^-1(x)=5^y

3.

Which graph represents the inverse function of f(x)=log₅x?

a)

b)

c)

d)

4.

If the asymptote of the function f is y=-2, what is the asymptote of its inverse function?

a)

y=2

b)

y=-2

c)

x=2

d)

x=-2

5.

If the domain and range of the function f is: Domain: x=3, Range: ℝ,

what is the domain and range of its inverse function?

a)

Domain: x=3

Range: ℝ

b)

Domain: y=3

Range: ℝ

c)

Domain: ℝ

Range: y=3

d)

Domain: ℝ

Range: x=3

6.

If the key points of the function f is (-1, 1⁄3); (0, 2); (1, 12),

what are the key points of its inverse function?

a)

(1⁄3, -1); (2, 0);

(12, 1)

b)

(-1, 1⁄3); (0, 2);

(1, 12)

c)

(-1, 12); (0, 1⁄3);

(1, 2)

d)

(1⁄3, 1); (2, 0);

(12, -1)

7.

Which of the following is equivalent to $5^2=25$

a)

$\log_525=2$

b)

$\log_225=5$

c)

$\log_{25}5=2$

d)

$\log25=2$

8.

Which of the following statements is true if $\log_2x=4.$

a)

$2^4=x$

b)

$x^4=2$

c)

$4^2=x$

d)

$x^2=4$ l

9.

Rewrite the equation into logarithmic form:

6² = 36

a)

log₆ 2 = 36

b)

log₆ 36 = 2

c)

ln 36 = 2

d)

6³⁶ = 2

10.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

11.

Write in logarithmic form. $3^4=81$

a)

$\log_381=4$

b)

$\log_{81}4=3$

c)

$\log_481=3$

12.

What is the base when you convert to exponential form:

\log_2x=3

(a)

13.

What is the exponent when you convert to exponential form:

$\log_7x=5$

(a)

14.

What is the base when you convert to logarithmic form:

$3^x=81$

(a)

15.

When you convert to logarithmic form, what is the function equal to?

$7^5=16807$

(a)

16.

What is the base when you convert to exponential form:

$\log_41=0$

(a)

17.

Select all the transformations that apply.

y = -2 log _1/2x

a)

Vertical stretch by 2

b)

Vertical shrink by 1/2

c)

Reflection across the y-axis

d)

Reflection across the x-axis

18.

Match the graph with its equation

a)

y = log₅ (x + 1) + 1

b)

y = log₅ (x - 1) + 1

c)

y = log₅ (x²) + 1

d)

y = log₅ (x)-1

19.

What is the equation of the asymptote?

a)

x = -3

b)

x=5

c)

y= -3

d)

y=5

20.

Describe the graph of f(x) = log x changed to

f(x) = 3log(x + 1) - 5

a)

vertical stretch by 3 and shift right 1 and 5 units down

b)

vertical stretch by 3 and shift left 1 and 5 units down

c)

vertical compress by 3 and shift right 1 and 5 units down

d)

vertical compress by 3 and shift left 1 and 5 units down

21.

Which has a vertical asymptote?

a)

Exponential

b)

Logarithmic

c)

Both

22.

Describe the transformations of f(x)= -log₂(x+1)

a)

left one & y-axis reflection

b)

right one & y-axis reflection

c)

left one & x-axis reflection

d)

right one & x-axis reflection

23.

What is the y-intercept of the function?

a)

2

b)

3

c)

1

d)

-2

24.

Is this exponential growth or decay?

a)

Growth

b)

Decay

25.

Where is the asymptote located?

a)

y = 1

b)

y = 0

c)

x = 0

d)

y = -1

26.

What is the transformation?

a)

Shifted up 2 and shifted right 1

b)

Shifted down 2 and shifted left 1

c)

Shifted left 2 and shifted up 1

d)

Shifted right 2 and shifted down 1

27.

Which graph best represents

y=2^x-4

a)

b)

c)

d)

28.

Which of the following function best represents this graph?

a)

$g\left(x\right)=2^x+2$

b)

$k\left(x\right)=-2^x+2$

c)

$m\left(x\right)=-2^x-2$

d)

$f\left(x\right)=0.5^x+2$

29.

Which of the following describes the transformation of $f\left(x\right)=\frac{1}{2}\cdot2^{\left(x+2\right)}-3$ from the parent graph $g\left(x\right)=2^x$

a)

Vertically shift down 3, horizontally shift left 2, and vertically compressed 1/2 units

b)

Vertically shift up 3, horizontally shift left 2, and vertically compressed 1/2 units

c)

Vertically shift down 3, horizontally shift right 2, and vertically compressed 1/2 units

d)

Vertically shift up 3, horizontally shift right2, and vertically compressed 1/2 units

30.

What is the equation for the asymptote for the graph of $f\left(x\right)=2^{\left(x-3\right)}$ ?

a)

$x=0$

b)

$y=0$

c)

$x=3$

d)

$y=2$

31.

What is the y-intercept of the function?

a)

(0, -3)

b)

(-3, 0)

c)

(1, 0)

d)

(0, 1)

32.

What is the domain of the function shown below?

a)

-2 < x < 5

b)

0 < x < 12

c)

y > 0

d)

All Real Numbers

33.

What is the value of the y-intercept of the graph of the graph of

h\left(x\right)=29\left(5.2\right)^x

?

a)

29

b)

1

c)

5.2

d)

0

34.

The graph of an exponential function is shown on the grid.

Which dashed line is an asymptote for the graph?

a)

Line $q$

b)

Line $r$

c)

Line $s$

d)

Line $t$

35.

a)

growth

b)

decay

36.

What is the asymptote of: $f\left(x\right)=2^{x+1}-3$

a)

$y=3$

b)

$y=0$

c)

$y=-3$

d)

$x=1$

37.

What transformations were made on $f\left(x\right)=10^x$ to produce $h\left(x\right)=\frac{1}{2}\left(10\right)^{x-2}+3$

a)

vertical compression by 1/2, left 2, up 3

b)

vertical compression by 1/2, right 2, up 3

c)

vertical compression by 1/2, right 2, down 3

d)

vertical stretch by 10, left 2, up 3

38.

Which statement about the graph of

y=\frac{1}{3}\left(\frac{2}{3}\right)^x

is true?

a)

The graph has a vertical asymptote.

b)

The graph crosses the y-axis at $\left(0,\frac{2}{9}\right)$ .

c)

The graph has an asymptote at $y=\frac{1}{3}$

d)

The graph decreases from left to right.

39.

What are the 3 anchor points of y= 4^x+10

a)

$\left(-1,\ \frac{1}{4}\right),\ \left(0,\ 11\right),\ \left(1,\ 14\right)$

b)

$\left(-1,\ \frac{41}{4}\right),\ \left(0,\ 11\right),\ \left(1,\ 14\right)\$

c)

$\left(-1,\ -\frac{39}{4}\right),\ \left(0,\ -9\right),\ \left(1,\ -6\right)$

d)

$\left(1,\ \frac{1}{4}\right),\ \left(0,\ -1\right),\ \left(-1,\ 4\right)$

40.

What are the 3 anchor points of the function $y=\log_4\left(x+2\right)$ ?

a)

$\left(-3,\ 4\right),\ \left(-2,\ 1\right),\ \left(-1,\ \frac{1}{4}\right)\$

b)

$\left(-\frac{7}{4},\ -1\right),\ \left(-1,\ 0\right),\ \left(2,\ 1\right)$

c)

$\left(\frac{1}{4},\ -1\right),\ \left(0,\ 1\right),\ \left(4,\ 1\right)$

d)

$\left(\frac{9}{4},\ -1\right),\ \left(1,\ 0\right),\ \left(4,\ 1\right)$

Unit 6b Test Review

Total questions: 40

Worksheet time: 54mins

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