Free Printable PreCalculus Final Exam Things to Know Cold

1.

$f\left(x\right)=\frac{1}{x-5}$ Find the domain of f(x).

a)

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

b)

$\left[5,\infty\right)$

c)

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

d)

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

2.

Write the domain of $f\left(x\right)=\frac{x}{x^2-16}$

a)

$\left(-\infty,0\right)U\left(4,\infty\right)$

b)

$\left[4,\infty\right)$

c)

$\left(-\infty,0\right)U\left(0,4\right]$

d)

$\left(-\infty,-4\right)U\left(-4,4\right)U\left(4,\infty\right)$

3.

Find the domain of $g\left(x\right)=\sqrt{2x-4}$

a)

$\left(-\infty,2\right)\left(2,\infty\right)$

b)

$\left[2,\infty\right)$

c)

$\left(-\infty,2\right]$

d)

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

4.

Even, odd, or neither?

a)

Even

b)

Odd

c)

Neither

5.

The function in the graph is:

a)

Even

b)

Odd

c)

Neither

6.

Is this an even, odd, or neither function?

f(x) = x⁴ + x²

a)

Even

b)

Odd

c)

Neither

7.

Name the discontinuity at x=2.

a)

Infinite Nonremovable Discontinuity

b)

Point Removable Discontinuity

c)

Jump Nonremovable Discontinuity

d)

Continuous at x=2

8.

Name the discontinuity at x=2.

a)

Infinite Nonremovable Discontinuity

b)

Point Removable Discontinuity

c)

Jump Nonremovable Discontinuity

d)

Continuous at x=2

9.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

10.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

11.

What is the name of the parent function and equation for the graph?

a)

Quadratic - $y=x^{2\ }$

b)

Absolute Value - $y=|x|$

c)

Square Root - $y=\sqrt{x}$

d)

Cube Root - $y=\sqrt[3]{x}$

12.

What is the name of the parent function and equation for the graph?

a)

Cubic - $y=x^{3\ }$

b)

Cube Root - $y=\sqrt[3]{x}$

c)

Exponential - $y=2^x$

d)

Logarmithic - $y=\log x$

13.

What is the name of the parent function and equation for the graph?

a)

Cube Root - $y=\sqrt[3]{x}$

b)

Cubic - $y=x^3$

c)

Exponential - $y=2^{x\ }$

d)

Rational/Inverse - $y=\frac{1}{x}$

14.

What is the name of the parent function and equation for the graph?

a)

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

b)

Absolute Value - $y=\left|x\right|$

c)

Linear - $y=x$

d)

Quadratic - $y=x^{2\ }$

15.

What is the name of the parent function and equation for the graph?

a)

Square Root - $y=\sqrt[]{x}$

b)

Exponential - $y=2^x$

c)

Logarithmic $y=\log x$

d)

Cube Root - $y=\sqrt[3]{x}$

16.

Which transformation will occur if f(x) = x² is replaced with f(x) + 2?

a)

Translation left 2 units

b)

Narrower

c)

Vertical translation up by 2 units.

d)

Reflection across the x-axis.

17.

Which transformation will occur if f(x) = x² is replaced with 1/2⋅f(x)?

a)

Vertical Dilation by a factor of 1/2

b)

Horizontal Dilation by a factor of 1/2

c)

Vertical translation up by 2 units.

d)

Reflection across the x-axis.

18.

Which transformation maps the graph of
f(x) = x² to the graph of g(x) = (x + 4)²?

a)

a translation shifting f(x) 4 units up

b)

a translation shifting f(x) 4 units down

c)

a translation shifting f(x) 4 units to the left

d)

a translation shifting f(x) 4 units to the right

19.

Describe the transformation of y = f(x) for the new function
y = 5f(x)

a)

Vertical Dilation by 5

b)

Vertical Dilation by 1/5

c)

Horizontal Dilation by 5

d)

Horizontal Dilation by 1/5

20.

Describe the transformation of y = f(x) for the new function
y = - f(x)

a)

The graph of y = f(x) was reflected vertically across the x axis.

b)

The graph of y = f(x) was reflected horizontally across the y axis.

c)

The graph of y = f(x) was shifted down.

d)

The graph of y = f(x) was shifted up

21.

Describe the transformation of y = f(x) for the new function
y = f(- x)

a)

The graph of y = f(x) was reflected vertically across the x axis.

b)

The graph of y = f(x) was reflected horizontally across the y axis.

c)

The graph of y = f(x) was shifted down.

d)

The graph of y = f(x) was shifted up

22.

tanθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

23.

What quadrant is -2π/3 in?

a)

I

b)

II

c)

III

d)

IV

24.

sinθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

25.

sin $\frac{\pi}{2}$

a)

$\frac{\sqrt[]{3}}{2}$

b)

$\frac{\sqrt[]{2}}{2}$

c)

$\frac{1}{2}$

d)

1

26.

cos $\frac{\pi}{4}$

a)

$\frac{\sqrt[]{3}}{2}$

b)

$\frac{\sqrt[]{2}}{2}$

c)

$\frac{1}{2}$

d)

1

27.

cos(π)

a)

$\frac{\sqrt[]{3}}{2}$

b)

$-\frac{\sqrt[]{2}}{2}$

c)

-1

d)

1

28.

cos $\frac{\pi}{6}$

a)

$\frac{\sqrt[]{2}}{2}$

b)

$-\frac{1}{2}$

c)

$\frac{1}{2}$

d)

$\frac{\sqrt[]{3}}{2}$

29.

tan 0

a)

undefined

b)

1

c)

0

d)

-1

30.

cosine is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

31.

$\tan\theta\ =$

a)

$\frac{\sin\theta}{\cos\theta}$

b)

$\frac{\cos\theta}{\sin\theta}$

c)

$\frac{1}{\cos\theta}$

d)

$\cot\theta$

32.

*

a)

sin x

b)

cos x

c)

tan x

d)

csc x

33.

What is csc(x) equivalent to?

a)

1/sin(x)

b)

1/tan(x)

c)

sin(x)

d)

1/cos(x)

34.

Which of the following is NOT a pythagorean identity?

a)

sin²x + cos²x = 1

b)

1 - cos²x = sin²x

c)

1 - sin²x = cos² x

d)

sin²x - cos²x = -1

35.

csc x =

a)

1/cosx

b)

1/sinx

c)

cot²x-1

d)

1/secx

36.

sec x =

a)

1/cosx

b)

1/sinx

c)

1/cscx

d)

1/tanx

37.

cos x =

a)

sin x

b)

sin²x-1

c)

1/sec x

d)

1/csc x

38.

sin x =

a)

cos x

b)

1/cosx

c)

1/secx

d)

1/cscx

39.

State the quadrant in which the terminal side of the angle lies. $\frac{7\pi}{6}$

a)

Q1

b)

Q2

c)

Q3

d)

Q4

40.

State the quadrant in which the terminal side of the angle lies. $\frac{5\pi}{4}$

a)

Q1

b)

Q2

c)

Q3

d)

Q4

41.

State the quadrant in which the terminal side of the angle lies. $-\frac{7\pi}{6}$

a)

Q1

b)

Q2

c)

Q3

d)

Q4

42.

State the quadrant in which the terminal side of the angle lies. $\frac{5\pi}{3}$

a)

Q1

b)

Q2

c)

Q3

d)

Q4

43.

State the quadrant in which the terminal side of the angle lies. $\frac{3\pi}{4}$

a)

Q1

b)

Q2

c)

Q3

d)

Q4

44.

State the quadrant in which the terminal side of the angle lies. $\frac{\pi}{4}$

a)

Q1

b)

Q2

c)

Q3

d)

Q4

45.

Select the graph of the angle in standard position:
$\frac{2\pi}{3}$

a)

b)

c)

d)

46.

Select the graph of the angle in standard position: $\frac{5\pi}{3}$

a)

b)

c)

d)

47.

Select the graph of the angle in standard position: $\frac{11\pi}{6}$

a)

b)

c)

d)

48.

Select the graph of the angle in standard position: $\frac{3\pi}{4}$

a)

b)

c)

d)

49.

Select the graph of the angle in standard position: $\frac{5\pi}{4}$

a)

b)

c)

d)

50.

Select the graph of the angle in standard position: $\frac{4\pi}{3}$

a)

b)

c)

d)

51.

Select the graph of the angle in standard position: $-\frac{5\pi}{2}$

a)

b)

c)

d)

52.

Sine or Cosine?

a)

y=sinx

b)

y=cosx

53.

Sine or Cosine?

a)

y=sinx

b)

y=cosx

54.

The __________ represents half the distance between the max and min of a sine or cosine graph.

a)

Period

b)

Frequency

c)

Extreme Values

d)

Amplitude

55.

What is the amplitude of the graph?

a)

1

b)

3

c)

6

d)

9

56.

Calculate the amplitude of the curve

a)

$2\pi$

b)

2

c)

1

d)

0

57.

Calculate the period of the curve

a)

$4\pi$

b)

$2\pi$

c)

2

d)

0

58.

Calculate the period of the curve

a)

$4\pi$

b)

$2\pi$

c)

1

d)

-1

59.

What is the period of y=4cos5x

a)

2π/5

b)

π

c)

5

d)

5π

60.

Solve on the domain [0,2π)
cos x + 1 = 0

a)

0

b)

No solution

c)

π

d)

3π/2

61.

Solve sinθ = ½ on [0, 2π)

a)

θ = π / 6, 7π / 6

b)

θ = π / 6, 5π / 6

c)

θ = 5π / 6, 7π / 6

d)

θ = 7π / 6, 11π / 6

62.

Solve $\cos\theta=-\frac{\sqrt[]{3}}{2}$
on [0, 2π)

a)

$θ=\frac{\pi}{3},\frac{2\pi}{3}$

b)

$θ=\frac{2\pi}{3},\frac{4\pi}{3}$

c)

$θ=\frac{\pi}{6},\frac{5\pi}{6}$

d)

$θ=\frac{5\pi}{6},\frac{7\pi}{6}$

63.

Factor: 8x³ - 1

a)

(2x - 1)(4x² + 2x + 1)

b)

(2x + 1)(4x² - 2x + 1)

c)

(2x - 1)(4x² - 2x - 1)

d)

(2x + 1)(4x² +2x + 1)

64.

Factor: x³+ 1

a)

(x + 1)³

b)

(x+1)(x²- x + 1)

c)

(x - 1) (x² + x - 1)

d)

(x + 1)(x² - 2x + 1)

65.

Write the equation of the circle.

a)

(x+1)² + (y +1)² = 3

b)

(x+1)² + (y -1)² = 3

c)

(x+1)² + (y +1)² = 9

d)

(x-1)² + (y -1)² = 9

66.

Write the equation in point-slope form of the line that passes through the point (4,-7) and has a slope of -1/4

a)

$y+7=-\frac{1}{4}(x-4)$

b)

$y-4=-\frac{1}{4}(x+7)$

c)

$y+7=4(x-4)$

d)

$y-7=-\frac{1}{4}(x-4)$

67.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

68.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

69.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

70.

Based on the end behavior of the polynomial, what best describes the leading coefficient?

a)

a negative real number

b)

a positive real number

c)

an even real number

d)

an odd real number

71.

Based on the end behavior of the polynomial, what is the degree of the polynomial?

a)

a negative real number

b)

a positive real number

c)

an odd real number

d)

an even real number

72.

What are the linear terms of the polynomial function?

a)

(x-2)(x-1)(x+1)(x-2)

b)

(x-2)(x-1)(x+1)(x+2)

c)

(x-2)(x-1)(x+1)(x+2)(x-4)

d)

(x-2)(x-1)(x+1)(x+2)(x+4)

73.

Based on the end behavior which option best describes the leading term?

a)

negative coefficient, even degree

b)

negative coefficient, odd degree

c)

negative degree, odd coefficient

d)

negative degree, even coefficient

74.

What are the zeros of the polynomial?

a)

$x=5,x=-3$ (multiplicity of 2)

b)

$x=-3,\ x=5$ (multiplicity of 2)

c)

$x=3,\ x=-5$

d)

$x=5$

75.

What are the vertical and horizontal asymptotes of the following function?

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

a)

VA: x=3

HA: y=1

b)

VA: x=1

HA: y=3

c)

VA: x=1

HA: y=-3

d)

VA: x = -1/3

HA: y=1

e)

VA: x=3

HA: y= -1/3

76.

What are the vertical and horizontal asymptotes of the following function?

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

a)

HA: y = -2

VA: x = 2

b)

HA: y = 2

VA: x = -2

c)

HA: y = -6

VA: x = 2

d)

HA: y = 1/2

VA: x = -6

e)

HA: y = 2

VA: x = -1/2

77.

What are the coordinates of the y-intercept, if one exists.

a)

(0, 0)

b)

(0, 1)

c)

(0, -1)

d)

there isn't one

78.

Find the x-intercept(s), if one exists.

a)

(1, 0)

b)

(-1, 0)

c)

(1, 0), (-1, 0)

d)

(0, 0), (1, 0)

79.

What is the equation of the vertical asymptote?

a)

x = 0

b)

x = 4

c)

x = -1, x = 4

d)

x = -1

80.

What is the equation of the horizontal asymptote?

a)

y = 0

b)

y = -2

c)

y = 2

d)

There isn't one

81.

What is the x-coordinate of the hole, if one exists?

a)

-4

b)

-3

c)

3

d)

there isn't one

82.

Rewrite as an exponential: log₂8 = 3

a)

3² = 8

b)

2³ = 8

c)

2⁸ = 3

d)

8³ = 2

83.

Rewrite as an exponential: $\log_7\left(\frac{1}{49}\right)=-2$

a)

$7^{\frac{1}{49}}=-2$

b)

$\left(\frac{1}{49}\right)^{-2}=7$

c)

$7^{-2}=\frac{1}{49}$

d)

$\left(-2\right)^7=\frac{1}{49}$

84.

Rewrite as a log: x = 11^y

a)

log₁₁(y) = x

b)

log_y(11) = x

c)

log₁₁(x) = y

d)

log_x(y) = 11

85.

Use multiple log properties to write as a single log:
log₂x - 5log₂y

a)

log₂(x/y⁵)

b)

log₂(xy⁵)

c)

log₂(x/y)⁵

d)

log₂(x/5y)

86.

Condense the logarithms.

$6\log x-3\log y$

a)

log (xy³)

b)

log (x⁶− y³)

c)

log (x⁶/y³)

d)

log (x⁶ + y³)

PreCalculus Final Exam Things to Know Cold

Total questions: 86

Worksheet time: 3hrs 21mins

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