Free Printable (HPC) 1.8 and Chapter 3 Test Review

1.

What does it mean to find the inverse of a function?

a)

the x's and y's are switched

b)

the x's and y's are divided by 2

c)

the x's and y's are made negative

d)

the x's and y's are the same

2.

The inverse has been reflected over which line?

a)

y = x

b)

y =1

c)

y = 0

d)

y = x + 1

3.

a)

b)

c)

d)

4.

a)

b)

c)

d)

5.

If the equation of f(x) goes through (1, 4) and (4, 6), what points does f^-1(x) go through?

a)

(1, 4) and (4, 6)

b)

(-4, -1) and (-6, -4)

c)

(-1, -4) and (-4, -6)

d)

(4, 1) and (6, 4)

6.

Find the inverse of

f(x) = (1/4)x - 7

a)

f^-1(x) = 4x + 7

b)

f^-1(x) = -4x + 28

c)

f^-1(x) = -4x - 7

d)

f^-1(x) = 4x + 28

7.

Determine f^-1(2) given the following information about an invertible function, f(x)
f(1) = -3
f(2) = -2
f(-1) = 2
f(3) = -1

a)

1

b)

-1

c)

2

d)

-2

8.

If f and g are inverse functions, and

f(2) = -1 g(1) = -2 f(1) = -2,

then which of the following MUST be true?

a)

g(-2) = -1

b)

g(2) = 1

c)

g(-2) = 1

d)

g(1) = 2

e)

None of the above

9.

If a function's inverse is also a function, what is true about the original function.

a)

It passes through (0,1)

b)

It is one-to-one

c)

It passes the diagonal line test

d)

It has an infinite domain

10.

What is the x-intercept of the exponential function?

a)

(0,1)

b)

(0,0)

c)

There is not one

11.

On the graph y =3^x + 4,

What is the equation of the asymptote

a)

y = 0

b)

y = 3

c)

y =4

d)

(0,3)

12.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

13.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

14.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

15.

How are exponential and logarithmic functions related?

a)

Opposites

b)

Inverses

c)

Cousins

d)

Reciprocals

16.

Rewrite log₂8 = 3 in exponential form.

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

e)

None of the above

17.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

18.

log₅25 = ?

a)

2

b)

5

c)

125

d)

10

19.

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

20.

Which equation is the inverse of the equation above?

a)

b)

c)

d)

21.

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

a)

b)

c)

d)

e)

None of the above

22.

Which graph best represents the following logarithmic function?
$y=\log_2x$

a)

b)

c)

d)

23.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

24.

The natural logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

25.

Evaluate log₄1

a)

1

b)

0

c)

4

d)

undefined

26.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

27.

Evaluate.

\log_2\left(\frac{1}{8}\right)

a)

1/2

b)

4

c)

-3

d)

-4

28.

Evaluate.

\log_{27}\ 3

a)

1/2

b)

-9

c)

1/3

d)

9

e)

None of the above

29.

Evaluate.

\log_4\left(\frac{1}{2}\right)

a)

1/2

b)

-2

c)

2

d)

-1/2

30.

Evaluate.

\ln e^4

a)

4

b)

e^4

c)

e

d)

ln e

31.

Evaluate.

10^{\log15}

a)

150

b)

10

c)

$\log15$

d)

15

32.

Evaluate.

\log0

a)

-1

b)

0

c)

1

d)

1/10

e)

None of the above

33.

Evaluate.
$\log_3\left(\frac{1}{\sqrt{3}}\right)$

a)

-1

b)

-1/3

c)

1/2

d)

1

e)

None of the above

34.

What is the domain of the following function?

f\left(x\right)=\log_5\left(6-x\right)

a)

(5,inf)

b)

(-inf,5)

c)

(6,inf)

d)

(-inf,6)

e)

None of the above

35.

What is the y-intercept of the following function?

f\left(x\right)=7^x+4

a)

4

b)

5

c)

6

d)

7

36.

Without graphing, where is the asymptote of the following function?

g\left(x\right)=\log_6\left(x-6\right)+4

a)

y=4

b)

y=6

c)

x=4

d)

x=6

e)

None of the above

37.

Find the inverse of the following function.

f\left(x\right)=\sqrt{x-4}+2

a)

$f^{-1}\left(x\right)=\left(x-2\right)^2+4;\ x\ge4$

b)

$f^{-1}\left(x\right)=\left(x-2\right)^2+4;\ x\ge2$

c)

$f^{-1}\left(x\right)=\left(x+2\right)^2+4;\ x\le4$

d)

$f^{-1}\left(x\right)=\left(x+2\right)^2+4;\ x\ge4$

e)

$f^{-1}\left(x\right)=\left(x+2\right)^2+4;\ x\ge2$

38.

What domain restriction will the inverse function need?

f\left(x\right)=-\sqrt{x}+5

a)

$x\ge0$

b)

$x\le0$

c)

$x\ge-5$

d)

$x\le5$

e)

None of the above

39.

Describe the transformation that occurred

p(x) = f(x + 3)

a)

Right 3 units

b)

Vertical Stretch

c)

Up 3 units

d)

Left 3 units

40.

Describe the transformation that occurred.

h(x) = f(x) + 2

a)

up 2 units

b)

left 2 units

c)

Vertical Strech

d)

right 2 units

41.

Which of the following is a transformation used in the function $f\left(x\right)=2\cdot6^{\left(x-4\right)}+3$

a)

Right 3 units

b)

Horizontal stretch by a factor of 2

c)

Left 4 units

d)

Horizontal shrink by a factor of 2

e)

Right 4 units

42.

Which of the following is a transformation used in the function $g\left(x\right)=-\log_2\left(3x\right)-8$

a)

Reflection over the x-axis

b)

Right 8 units

c)

Vertical stretch by a factor of 3

d)

Horizontal shrink by a factor of 2

e)

Up 8 units

43.

Let the point (x,y) be a point on the graph of f(x). How will the point be changed if the graph of f(x) undergoes the following transformation:

Left 6 units

a)

(x/6,y)

b)

(x,6y)

c)

(x-6,y)

d)

(x,y-6)

44.

Let the point (x,y) be a point on the graph of f(x). How will the point be changed if the graph of f(x) undergoes the following transformation:

Vertical shrink by a factor of 1/3

a)

(3x,y)

b)

(x,y/3)

c)

(x,3y)

d)

(x/3,y)

45.

Which transformation is performed third?

a)

Reflection

b)

Horizontal Shift

c)

Vertical Shift

d)

Stretch/Shrink

46.

Find the accumulated value of an investment of $6000 for 3 years at an interest rate of 1.8% if the money is compounded monthly.

a)

$6240.98

b)

$6332.65

c)

$8012.34

d)

$10254.84

e)

None of the above

47.

Find the accumulated value of an investment of $13000 for 8 years at an interest rate of 0.8% if the money is compounded semiannually.

a)

$13857.43

b)

$14023.01

c)

$14590.23

d)

$15480.85

e)

None of the above

48.

Find the accumulated value of an investment of $10000 for 20 years at an interest rate of 0.5% if the money is compounded continuously.

a)

$11051.71

b)

$11702.45

c)

$12793.56

d)

$13409.37

e)

None of the above

49.

Consider the function $f\left(x\right)=\frac{1}{x-4}$ .
What is the range of its inverse function?

a)

(-inf,inf)

b)

(4,inf)

c)

(-inf,0)

d)

(-inf,4)u(4,inf)

e)

None of the above

50.

If a one-to-one function has a domain of (-inf, inf), passes through the points (-1,4), (0,1), (2,0.5), (5,0), and (8,-3), and has a horizontal asymptote at y=-4, what is the y-intercept of the graph of its inverse function?

a)

-4

b)

1

c)

4

d)

5

e)

None of the above

51.

Simplify log(12) + log (6)

a)

log(72)

b)

log(18)

c)

log(6)

d)

log(2)

52.

Simplify: log(3) + 2log(5)

a)

log(75)

b)

2log(15)

c)

log(30)

d)

log(13)

53.

Simplify: 2log(x) + 3log(xy)

a)

log(x⁵y³)

b)

log(5xy)

c)

5log(x²y)

d)

log(6x²y)

54.

What is the most simple answer possible:
log_x(x³y) - log_x(xy)

a)

log_x(x²)

b)

2

c)

log_x(x⁴-y²)

d)

x

55.

Evaluate log_b(b^x)

a)

1

b)

0

c)

x

d)

b

56.

Evaluate log_b(b)

a)

-1

b)

0

c)

1

d)

b

57.

Evaluate log_b(1)

a)

0

b)

1

c)

-1

d)

b

58.

a)

log(x) + log(z) + 4log(y)

b)

3log(x) − log(z) − 4log(y)

c)

3log(x) + log(z) + 4log(y)

d)

log(x) − 4log(z) − 3log(y)

59.

Write the expression as a single logarithm. Then simplify if possible.

log₅3 + log₅6 - log₅9

a)

log₅0

b)

log₅56

c)

log₅2

d)

log₅98

60.

(log a)(log b) = log (a+b)

a)

True

b)

False

61.

Expand

a)

6log₈v-2log₈u

b)

6log₈u-2log₈v

c)

3log₈u-2log₈v

d)

6log₈u+2log₈v

62.

Condense

a)

logxyz³

b)

log(xy/z³)

c)

logx+logy+logz³

d)

logx³y³z³

63.

a)

5log₆(a) + 6log₆(c) − 30log₆(b)

b)

log₆(a) + 6log₆(c) − 5log₆(b)

c)

6log₆(a) − 6log₆(c) − 30log₆(b)

d)

6log₆(a) + 6log₆(c) − 30log₆(b)

64.

a)

log₅(x²z²y¹⁰)

b)

log₅(z²y²x¹⁰)

c)

log(zy²x¹⁰)

d)

log₅(z² + y²+ x¹⁰)

65.

Simplifying using the laws of logarithms

a)

log(10)

b)

log(3)

c)

log(20)

d)

log(75)

66.

Evaluate

a)

2

b)

4

c)

-2

d)

1

67.

Simplifying using laws of logarithms

a)

log(31)

b)

log(108)

c)

5log(6)

d)

5log(5)

68.

3^{2x – 6} = 81

a)

x = log 4

b)

x = 5

c)

x = 4

d)

x = -1

69.

log₂(2) + log₂(8x) = 6

a)

x = 3

b)

x = 2

c)

x = 6

d)

x = 4

70.

log₆(2x + 3) = 3

a)

x = 106.5

b)

x = 100

c)

x = 16

d)

x = 50

71.

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

72.

To solve, 16^5x = 64^x+7, what would be the correct set-up?

There is more than one correct answer.

a)

4^4(5x)=4^16(x+7)

b)

8^2(5x)=8^8(x+7)

c)

4^2(5x)=4^3(x+7)

d)

2^4(5x)=2^6(x+7)

73.

Solve the equation for x.

a)

22.198

b)

e

c)

1.131

d)

21.66

74.

a)

A

b)

B

c)

C

d)

D

75.

Solve:

log₉(x)+log₉(x+2)=log₉(35)

a)

5

b)

-7

c)

5, -7

d)

-7, -13

76.

Which is equivalent to the following equation?

2^3x+1= 12

a)

ln(2)= 3x+1

b)

log₂(12)= 3x+1

c)

ln(6)=3x+1

d)

log₁₂(2)= 3x+1

77.

Write an exponential function to model this situation:

$12,000 invested at a rate of 6% compounded quarterly

a)

$12000\cdot(1.06)^{4t}$

b)

$12000\cdot(1.015)^t$

c)

$12000\cdot(1.015)^{4t}$

d)

$12000\cdot(1.06)^t$

78.

What will the balance be if $500 is invested at a rate of 2.5% compounded annually, after 10 years?

a)

$4,656.61

b)

$640.04

c)

$1,280.08

d)

$2,560.16

(HPC) 1.8 and Chapter 3 Test Review

Total questions: 78

Worksheet time: 4hrs 47mins

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