Free Printable exam 1 trig review

1.

Slopes of parallel lines are _________.

a)

equal

b)

reciprocals

c)

opposite reciprocals

d)

unrelated

e)

negative

2.

Calculate the slope of the line passing through the points (2, 4) and (5, 10).

a)

$2$

b)

$\frac{3}{2}$

c)

$\frac{6}{5}$

d)

$\frac{5}{3}$

e)

$\frac{4}{3}$

3.

The line $x = 5$ ________.

a)

is vertical

b)

is horizontal

c)

has a slope of 5

d)

has a slope of 0

e)

is undefined

4.

What is the equation of the line that passes through the point (-3, 5) with a slope of 2?

a)

$y = 2(x - 3) + 5$

b)

$y-5=2(x+3)$

c)

$y + 3 = 2(x + 5)$

d)

$y-5=2(x-3)$

e)

$y + 5 = 2(x - 3)$

5.

If $h(x) = -x^2 + 6x - 2$ , find $h(3)$ .

a)

7

b)

11

c)

10

d)

5

e)

9

6.

If $g(x)=x^2-2x$ , find $g(x + 2)$ .

a)

$x^2+3x+4$

b)

$x^2 + x - 2$

c)

$x^2+2x$

d)

$x^2 + 5x + 2$

e)

$x^2 + 3x$

7.

Determine $f(3)$ for the given piecewise function.

a)

3

b)

-2

c)

-1

d)

4

e)

none of these

8.

For $g(x) = -x^2 + 5$ , determine the range.

a)

$(-\infty, 5]$

b)

$[5, \infty)$

c)

$(-5, \infty)$

d)

$(-\infty, \infty)$

e)

$(-\infty, 5)$

9.

Is this graph even, odd, or neither?

a)

even

b)

odd

c)

neither

10.

Which equation represents the transformation of the parent function y = x²?

a)

$y = (x - 3)^2 + 4$

b)

$y = (x + 3)^2 - 4$

c)

$y = (x - 3)^2 - 4$

d)

$y = x^2 - 3 + 4$

11.

Pick the composite function notation.

a)

$f(g(x))$

b)

$f(x) + g(x)$

c)

$f(x) \cdot g(x)$

d)

$f(x) + c$

e)

$\frac{f(x)}{g(x)}$

12.

Convert the quadratic function $y = x^2 + 6x + 8$ into its vertex form.

a)

$y = (x + 3)^2 - 1$

b)

$y = (x - 3)^2 + 1$

c)

$y = (x + 3)^2 + 1$

d)

$y = (x - 3)^2 - 1$

13.

Find the y-intercept of the line $y = 3x - 5$ .

a)

0

b)

5

c)

-5

d)

3

14.

Which of the following is the inverse function notation?

a)

$f(x) + g(x)$

b)

$1/f(x)$

c)

$f(x)^{-1}$

d)

$f^{-1}(x)$

15.

Find the equation of the line parallel to $y = 2x + 3$ passing through the point (1, 2).

a)

$y = 2x + 1$

b)

$y = 2x - 1$

c)

$y=2x$

d)

$y=-\frac{1}{2}x$

16.

What is the axis of symmetry for the quadratic function $y = x^2 - 4x + 3$ ?

a)

$x = -4$

b)

$x = 4$

c)

$x = -2$

d)

$x = 2$

17.

Determine the slope of the line perpendicular to $y = \frac{1}{2}x + 3$ .

a)

$2$

b)

$-2$

c)

$-\frac{1}{2}$

d)

$\frac{1}{2}$

18.

What is the domain of the function $f(x) = \frac{1}{x-3}$ ?

a)

$[3, \infty)$

b)

$(-\infty, 3]$

c)

$(-\infty, \infty)$

d)

$(-\infty, 3) \cup (3, \infty)$

19.

What is the range of the function $f(x) = x^2 - 5$ ?

a)

$[-5, \infty)$

b)

$[0, \infty)$

c)

$(-\infty, \infty)$

d)

$(-\infty, -5]$

e)

$\left(-5,\infty\right)$

20.

What is the function for this graph?

a)

$y=\sqrt[]{x}$

b)

y = 1/x

c)

y = |x|

d)

y = ln x

e)

y = x²

21.

What is the function for this graph?

a)

$y=\sqrt[]{x}$

b)

y = 1/x

c)

y = |x|

d)

y = ln x

e)

y = x²

22.

What is the function for this graph?

a)

$y=\sqrt[]{x}$

b)

y = 1/x

c)

y = |x|

d)

y = ln x

e)

y = x²

23.

What is the function for this graph?

a)

$y=\sqrt[]{x}$

b)

y = 1/x

c)

y = |x|

d)

y = ln x

e)

y = x³

24.

What is the function for this graph?

a)

$y=\sqrt[]{x}$

b)

y = 1/x

c)

y = |x|

d)

y = ln x

e)

y = x³

25.

What is the domain of f(g(x)) for f(x) = $\frac{1}{x+3}$ and g(x) = $\frac{1}{x+2}$ ?

a)

$x\ne-2$

b)

$x\ne-2,\ -\frac{7}{3}$

c)

$x\ne-2,-3$

d)

$x\ne-3$

e)

$x\ne-2,\ -\frac{3}{7}$

26.

Find g(f(2)) using the table.

a)

8

b)

2

c)

3

d)

1

e)

7

27.

What is the inverse of y = $\frac{7}{x+3}$

a)

y = $\frac{x+3}{7}$

b)

y = $\frac{x-3}{7}$

c)

y = $\frac{7}{x}-3$

d)

y = $\frac{x}{3}-7$

28.

If g(x) has the point (5, 7), what point must be on the inverse of g(x)?

a)

(7, 5)

b)

(-5, -7)

c)

(-7, 5)

d)

(5, -7)

e)

(0, 0)

29.

Factor this polynomial: x² - 10x + 25

a)

(x - 5)²

b)

(x - 1)(x - 25)

c)

(x + 5)²

d)

(x - 2)(x - 5)

e)

(x - 3)(x - 7)

30.

Complete the square: y = x² - 4x + 5

a)

y = (x - 2)² + 1

b)

y = (x + 2)² - 3

c)

y = (x - 2)² - 3

d)

y = (x + 2)² + 1

e)

y = (x - 4)² + 5

31.

Find the vertex: y = x² - 4x + 5

a)

(2, 1)

b)

(-2, 9)

c)

(0, 5)

d)

(1, 0)

e)

(-1, 10)

32.

Given x² - 4x + 4 = 0 and x · m = 1/2, find the value of m.

a)

1/2

b)

-1/2

c)

2

d)

1/4

e)

4

33.

Consider the function g(x) = 2x³ + 5x. What is the end behavior of this function?

As x $\rightarrow\infty$ , f(x) $\rightarrow$ (a) .

As x $\rightarrow-\infty$ , f(x) $\rightarrow$ (b)

Choose from the below words

$\infty$

$-\infty$

1

0

-1

34.

Multiply: (5 + 3i)(2 - i)

a)

13 + 7i

b)

11 - i

c)

7 + 11i

d)

10 + 5i

e)

13 + i

35.

What is the complex conjugate of 5 + 4i?

a)

-5 + 4i

b)

5 - 4i

c)

-5 - 4i

d)

4i - 5

e)

5 + 4i

36.

Find the product of 5 - 2i and its complex conjugate and simplify.

a)

29

b)

21

c)

25

d)

27

e)

31

37.

Use the quadratic formula to solve: x² + 4x + 5 = 0

a)

$-2\pm i$

b)

$-2\pm3i$

c)

$2\pm3i$

d)

$-2\pm\sqrt[]{3}i$

38.

An x-value that makes both the numerator and denominator of a rational function equal to zero is

a)

a horizontal asymptote.

b)

a vertical asymptote.

c)

a hole.

d)

in the domain.

39.

An x-value that makes only the denominator of a rational function equal to zero is

a)

a horizontal asymptote.

b)

a vertical asymptote.

c)

a hole.

d)

in the domain.

40.

Factor Completely.
8x³ - 18x

a)

2x(4x²-9)

b)

(4x²+3)(2x-3)

c)

2x(2x+3)(2x-3)

d)

PRIME

41.

Factor
x²+ 9x - 36

42.

Factor the Trinomial:
x² - 8x + 15

43.

Factor
3x² + 4x + 1

44.

Factor
x² -2x - 24

45.

which equation best fits this graph

a)

$y=a^x$

b)

$y=a^2$

c)

$y=mx+b$

d)

$y=\left|x\right|$

46.

In an exponential function, what does the 'a' represent?

a)

SLOPE

b)

RATE OF CHANGE

c)

Y-INTERCEPT

d)

COMMON RATIO

47.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

48.

What is the range for
f(x) = 5^x-6- 3?

a)

(3,∞)

b)

(-3,∞)

c)

(-∞, 3)

d)

(-∞, -3)

49.

What is the horizontal asymptote and what transformations have taken place?
y = 2^x+2 + 1

a)

y = 2
right 2, up 1

b)

y = 1
left 2, up 1

c)

y = 1
right 2, up 1

d)

y = 2
right 1, up 2

50.

Describe the transformation on

y=2\left(4\right)^x

when if becomes

y=2\left(4\right)^{\left(x-5\right)}

a)

Down 5

b)

Right 5

c)

Left 5

d)

Up 5

51.

Identify the domain of the exponential function: $y=5\left(\frac{1}{3}\right)^{\left(x-1\right)}$

a)

y > 1

b)

All real numbers

c)

y > -1

d)

x > -1

52.

Which function matches the graph?

a)

b)

c)

d)

53.

Choose ALL the transformations of $f\left(x\right)=3^x$ that creates $g\left(x\right)=3^{\left(x-4\right)}$

a)

Vertical Shift up 4

b)

Horizontal Shift left 4

c)

Vertical Shift down 4

d)

Horizontal Shift right 4

54.

Choose ALL the transformations of $f\left(x\right)=4^x$ that creates $g\left(x\right)=4^x+1$

a)

Vertical shift down 1

b)

Horizontal shift left 1

c)

Vertical shift up 1

d)

Horizontal shift right 1

55.

Which increases faster as $x\rightarrow\infty$ ?

a)

y = e^x

b)

y = 5^x

56.

Condense

$\log_39+\log_33$

a)

$\log_312$

b)

$\log_327$

c)

$\log_39$

57.

Condense

\log_5y-\log_525

a)

$\log_5\left(y-25\right)$

b)

$\log_5\left(25y\right)$

c)

$\log_5\left(\frac{y}{25}\right)$

d)

$\log_5\left(\frac{25}{y}\right)$

58.

Rewrite log_vn = a in exponential form.

a)

v^a = n

b)

n^a = v

c)

vⁿ = a

d)

aⁿ = v

59.

Condense: log₂6+log₂3=

a)

log₂18

b)

log₂2 = 1

c)

log₂3

d)

log₂9

60.

Rewrite in exponential form:
ln(2) = x

a)

2^x= 10

b)

10² = x

c)

e^x= 2

d)

e² = x

61.

Rewrite log_b(xⁿ)

a)

nlog_bx

b)

(log_bx)ⁿ

c)

xⁿlog_bx

d)

log_b(xⁿ)

62.

Find the value of: e^ln(f)

a)

f

b)

e

c)

e^f

d)

undefined

63.

Evaluate log₄1

a)

1

b)

0

c)

4

d)

undefined

64.

Find the exact value of: ln e⁵

a)

e⁵

b)

ln 5

c)

5

d)

5e

65.

Solve the exponential equation.

$19=e^{2x}$

a)

$\frac{\ln\left(19\right)}{2}$

b)

$\frac{\ln\left(19\right)}{\ln\left(2\right)}$

c)

$\frac{\ln\left(2\right)}{19\ln e}$

d)

$\approx4.248$

66.

Solve the logarithmic equation.

$\log_3\left(x\right)+8=11$

67.

log₇7³

a)

3

b)

343

c)

7

d)

21

68.

Simplify e^ln(x)

a)

0

b)

1

c)

x

d)

8

69.

Solve for x:

log₆x = -2

a)

6

b)

1/36

c)

36

d)

-6

70.

Write 5² = 25 in logarithmic form

a)

log₅ 2 = 25

b)

log₅ 25 = 2

c)

log₂ 25 = 5

d)

No Correct Answer

71.

Rewrite log₂8 = 3 in exponential form.

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

72.

Solve ln e

a)

10

b)

1

c)

5

d)

3

73.

ln(0) =

a)

undefined

b)

1

c)

-1

d)

1/2

e)

0

74.

ln(1) =

a)

0

b)

1

c)

-1

d)

1/2

e)

undefined

75.

Solve for x.

3³ = 3^{x + 2}

a)

x = 1

b)

x = -1

c)

x = ½

d)

x = -½

76.

Solve for x.

2^x+6 = 32

a)

x=-1

b)

x=11

c)

x=1

d)

x=-11

77.

Solve: 16 = 4^x+1

a)

x = -2

b)

x = 1

c)

x = -3

d)

x = 3

78.

Which of the following is the value of x given;
$e^{\left(x+6\right)\ }=\ 12$

a)

x = ln 6

b)

x = -6 + ln12

c)

x = ln72

d)

x = ln(-2)

79.

Solve for n:
2^-2n = 2⁶

a)

n = -1

b)

n = -7

c)

n = 5

d)

n = -3

80.

Use the change of base rule to rewrite this problem:

log₃64

a)

log(64)/log(3)

b)

log(3)/log(64)

81.

In Change of Base Formula, $\log_ba$ becomes:

a)

$\frac{\log\left(b\right)}{\log\left(a\right)}$

b)

$\frac{\ln\left(b\right)}{\ln\left(a\right)}$

c)

$\frac{\ln\left(a\right)}{\ln\left(b\right)}$

d)

$\ln\left(a\right)+\ln\left(b\right)$

e)

$\ln\left(a\right)-\ln\left(b\right)$

82.

If $\log_BA=\frac{\log_nA}{\log_nB}$ , then $\log_{25}3=$

a)

$\frac{\ln25}{\ln3}$

b)

$\ln\frac{25}{3}$

c)

$\frac{\ln3}{\ln25}$

d)

$\ln\frac{3}{25}$

83.

Use the change of base rule to rewrite this problem:

log₇256

a)

$\frac{\log_5\left(256\right)}{\log_3\left(7\right)}$

b)

$\frac{\log_2\left(256\right)}{\log_2\left(7\right)}$

c)

$\frac{\ln\left(7\right)}{\ln\left(256\right)}$

d)

$\frac{\ln\left(256\right)}{\log\left(7\right)}$

84.

Use the change of base rule to expand this problem:

$\log_{10}\left(9\right)$

a)

$\frac{\log\left(10\right)}{\ln\left(9\right)}$

b)

$\frac{\log\left(9\right)}{\ln\left(10\right)}$

c)

$\frac{\log_3\left(10\right)}{\log_3\left(9\right)}$

d)

$\frac{\ln\left(9\right)}{\ln\left(10\right)}$

85.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect!

86.

a)

2x³ + 3x + (7/x-4)

b)

2x² + 3x + 8 + (7/x-4)

c)

2x² + 3x + 8

d)

2x² - x + 10 + (6/x-4)

87.

What is the degree of f(x)?

f(x)=2x^3-3x^2+4x-10

a)

3

b)

2

c)

1

d)

0

88.

Find the Quotient (remainder not needed)
(2x³ - 5x² - 3x + 7) / (x - 2)

a)

2x²- 9x +15

b)

2x² - x - 5

c)

2x² - 9x - 21

d)

2x² + x + 5

89.

Find the quotient of the polynomials.

$\left(3d^2-4d+13\right)\div\left(d+3\right)$

a)

$3d-13+\frac{52}{d+3}$

b)

$3d-13+\frac{-26}{d+3}$

c)

$3d+5+\frac{-26}{d+3}$

d)

$d-13+\frac{26}{d+3}$

90.

Which term is missing in this problem?
2x³ + 5x² + 9 ÷
x + 3

a)

x⁴

b)

x³

c)

x²

d)

x

91.

a)

This is correct

b)

This is incorrect

92.

(4x² - 24x + 35) ÷ (2x - 5)

a)

2x - 7

b)

2x - 12

c)

2x + 12

d)

2x + 7

93.

(2x³ - 5x - 7) ÷ (x - 2)

a)

2x³ - 4x² + 3x - 13

b)

2x³ + 4x² +3x - 1

c)

2x² - 4x + 3 - 13/x-2

d)

2x² + 4x + 3 - 1/x-2

94.

$f\left(x\right)=\frac{x^2+3x-4}{3x^2+11x-4}$

The x-value of the hole in this equation is _

(a)

95.

What are the asymptotes for the graph pictured?

a)

x= 1

y= 1

b)

x= 0

y= 0

c)

none

d)

x= -1

y= 1

96.

Find the Vertical Asymptotes for the following function

g\left(x\right)\ =\frac{2x^2+x-9}{x^2-2x-8}

a)

$x=-4,\ x=2$

b)

$x=-2,\ x=4$

c)

$x=-6,\ x\ =\ -2$

d)

$x=\ 2,\ x=6$

97.

Match the following

a)

$f\left(x\right)=\frac{6}{x-1}$

1.

HA at x-axis

b)

$f\left(x\right)=\frac{x+4}{x-5}$

2.

HA at y = 1

c)

$f\left(x\right)=\frac{-3x-1}{3x+2}$

3.

HA at y = -1

d)

$f\left(x\right)=\frac{6x+1}{3x-5}$

4.

HA at y = 2

e)

$f\left(x\right)=\frac{-8x+3}{4x}$

5.

HA at y = -2

98.

What is the x-value of the hole, if one exists.

a)

-2

b)

-1

c)

3

d)

there isn't one

e)

-3

99.

Vocabulary: The graph of a polynomial is __________, so it has no breaks, holes, or gaps.

a)

a glancing blow

b)

linear

c)

continuous

d)

multiplicified

100.

Determine the equations of any horizontal and vertical asymptotes of $f\left(x\right)=\frac{x^2-9}{x^2+3x-18}$

a)

HA: $y=6$

VA: $x=0$

b)

HA: $y=1$

VA: $x=-6$

c)

HA: $y=1$

VA: $x=3,\ -6$

d)

HA: $y=0$

VA: none

exam 1 trig review

Total questions: 100

Worksheet time: 3hrs 22mins

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