Free Printable Precal Final Exam Review

1.

Given the graph of a rational function that approaches $x = 3$ but never touches or crosses it, what is the vertical asymptote?

a)

$x = 2$

b)

$x = -2$

c)

$x = 3$

d)

$x = 0$

2.

What is the degree of the polynomial $f(x) = 4x^5 - 2x^3 + x - 7$ ?

a)

$1$

b)

$3$

c)

$4$

d)

$5$

3.

Which of the following describes the end behavior of $f(x) = -3x^4 + 2x^2 - 1$ ?

a)

Both ends up

b)

Both ends down

c)

Left up, right down

d)

Left down, right up

4.

Given $f(x) = x^3$ , is the function even, odd, or neither?

a)

Even

b)

Odd

c)

Neither

d)

Cannot be determined

5.

Which of the following is the inverse of $f(x) = 2x + 5$ ?

a)

$f^{-1}(x) = \frac{x-5}{2}$

b)

$f^{-1}(x) = 2x - 5$

c)

$f^{-1}(x) = \frac{x+5}{2}$

d)

$f^{-1}(x) = \frac{x}{2} + 5$

6.

What is the horizontal asymptote of $f(x) = \frac{2x^2 + 1}{x^2 - 3}$ ?

a)

$y = 2$

b)

$y = 1$

c)

$y = 0$

d)

$y = -3$

7.

The graph of a function crosses the x-axis at $x = -2$ and $x = 2$ . What are the zeros of the function?

a)

$x = 2, -2$

b)

$x = 4, -4$

c)

$x = 0, 4$

d)

$x = 0, -4$

8.

What is the leading coefficient of $f(x) = -5x^4 + 3x^2 - 7$ ?

a)

$-5$

b)

$3$

c)

$4$

d)

$-7$

9.

Which of the following functions has a slant (oblique) asymptote?

a)

$f(x) = \frac{x^2 + 1}{x^2 - 1}$

b)

$f(x) = \frac{x^3}{x^2}$

c)

$f(x) = \frac{x}{x^2 + 1}$

d)

$f(x) = \frac{1}{x}$

10.

Given $f(x) = \frac{(x-2)(x+1)}{(x-2)(x-3)}$ , what value of $x$ creates a hole in the graph?

a)

$x = -1$

b)

$x = 2$

c)

$x = 3$

d)

$x = 0$

11.

Given the graph of a cubic polynomial with zeros at $x = -2$ , $x = 1$ (multiplicity 2), which of the following could be its equation?

a)

$f(x) = (x+2)(x-1)^2$

b)

$f(x) = (x-2)(x+1)^2$

c)

$f(x) = (x+2)^2(x-1)$

d)

$f(x) = (x-2)^2(x+1)$

12.

Which of the following is NOT a parent function?

a)

$f(x) = x^3$

b)

$f(x) = |x|$

c)

$f(x) = x^2 + 1$

d)

$f(x) = \sqrt{x}$

13.

Which of the following is the correct equation for the inverse of $f(x) = \frac{x-3}{2}$ ?

a)

$f^{-1}(x) = 2x + 3$

b)

$f^{-1}(x) = 2x - 3$

c)

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

d)

$f^{-1}(x) = \frac{x-3}{2}$

14.

Which of the following best describes the end behavior of $f(x) = 2x^3 - x$ ?

a)

As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$

b)

As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$

c)

Both ends up

d)

Both ends down

15.

a)

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

b)

y = x(x - 3)²(x+2)

c)

y = x(x + 3)²(x - 2)

d)

y = -x(x + 3)²(x - 2)

16.

a)

y = ^_(x + 2)(x - 1)²

b)

y = -(x - 2)(x + 1)²

c)

y = (x - 2)(x + 1)²

d)

y = -x³

17.

Which is true about the equation of the graph shown?

a)

The function has an Odd degree

b)

The function has an Even degree

c)

The function has 5 real zeros

d)

The function has a positive leading coefficient

18.

Find the vertical asymptote.

f\left(x\right)=\frac{x^2-2x-8}{3x-2}

a)

y=2/3

b)

x=3/2

c)

x= 2/3

d)

x=1/3

19.

What is/are the Vertical Asymptote(s)?

a)

x= -4

b)

x= -4, x= 5

c)

x= -5, x= 5

d)

x= 4

20.

Select all the following statements that are true.

a)

Vertical asymptote at x=1

b)

Vertical asymptote at x=0

c)

No vertical asymptote

d)

Hole at (-1, 0)

e)

Hole at (1, -1)

21.

The polynomial is...

a)

Odd degree, positive leading coefficient.

b)

Odd degree, negative leading coefficient.

c)

Even degree, positive leading coefficient.

d)

Even degree, negative leading coefficient.

22.

a)

F

b)

G

c)

H

d)

J

23.

sin 0 =

a)

0

b)

¹/₂

c)

^√2/₂

d)

^√3/₂

e)

1

24.

cos π =

a)

0

b)

1

c)

-1

d)

undefined

25.

sec (-60) = ?

a)

2

b)

$\frac{-2\sqrt{3}}{3}$

c)

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

d)

-2

26.

$\sin\left(-135\degree\right)$

a)

$\frac{\sqrt{2}}{2}$

b)

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

c)

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

d)

$-\frac{\sqrt{3}}{2}$

27.

$\cos\ \left(-\frac{11\pi}{3}\right)$

a)

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

b)

$\frac{1}{2}$

c)

$-\frac{1}{2}$

d)

$-\frac{\sqrt{3}}{2}$

28.

Evaluate:

$\sin\left(-\frac{\pi}{2}\right)$

a)

$1$

b)

$0$

c)

$-1$

d)

Undefined

e)

2

29.

a)

No solution

b)

π/3 +2πn, 5π/3 +2πn

c)

π/6 +2πn, 11π/6 +2πn

d)

2π/3 +2πn, 4π/3 +2πn

30.

a)

A

b)

B

c)

C

d)

D

31.

Solve on [0, 2π)

$4\sin^2x=3$

a)

π/6, 11π/6

b)

π/3, 2π/3

c)

π/6, 5π/6, 7π/6, 11π/6

d)

π/3, 2π/3, 4π/3, 5π/3

32.

Solve equation on $0\le\theta<2\pi$ .

$1=5-8\cos\theta$

a)

$\theta=\frac{\pi}{6},\frac{\pi}{3},\frac{11\pi}{6}$

b)

$\theta=\frac{\pi}{6},\frac{11\pi}{6}$

c)

$\theta=\frac{\pi}{6}$

d)

$\theta=\frac{\pi}{3},\frac{5\pi}{3}$

33.

Solve equation on $0\le\theta<2\pi$ .

$3\sin^2\theta+4=5+\sin^2\theta$

a)

$\theta=\frac{\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}$

b)

$\theta=\frac{\pi}{4},\frac{7\pi}{4}$

c)

$\theta=\frac{\pi}{4},\frac{3\pi}{4}$

d)

$\theta=\frac{\pi}{4},\frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}$

34.

Solve equation for $0\le\theta<2\pi$ . $-\sin\theta\csc\theta+3\csc\theta=\sqrt{2}\sin\theta+3\csc\theta$

a)

$\theta=\frac{5\pi}{4},\frac{11\pi}{6}$

b)

$\theta=\frac{3\pi}{4},\frac{7\pi}{6},\frac{7\pi}{4}$

c)

$\theta=0,\pi,\frac{5\pi}{4},\frac{7\pi}{4}$

d)

$\theta=\frac{5\pi}{4},\frac{7\pi}{4}$

35.

Solve for the unknown variable on the interval 0≤x<2π

sinx + 2sinxcosx = 0

a)

2π/3, 4π/3, 0, π

b)

2π/3, 4π/3

c)

0, π

d)

π/3, 5π/3

36.

Solve for 0≤x≤2π

2sin²x - 5sinx + 2 = 0

a)

π/6, 5π/6

b)

7π/6, 11π/6

c)

π/3, 2π/3

d)

4π/3, 5π/3

37.

Solve on the interval $\left[0,2\pi\right)$

$2\cos^2\left(x\right)-3\cos\left(x\right)+1=0$

a)

$x=0,\frac{\pi}{3},\frac{5\pi}{3}$

b)

$x=\frac{\pi}{6},\frac{\pi}{2},\frac{11}{6}$

c)

$x=0,\pi,2\pi$

d)

$x=\frac{\pi}{6},\frac{\pi}{2},\frac{5\pi}{6}$

38.

Solve on the domain [0, 2π)
cos x + 2 = 3 cos x

a)

0, 2π/3, 4π/3

b)

π

c)

0

d)

No solution

39.

Let (-4, 3) be a point on the terminal side of θ. What is tan θ?

a)

-4/5

b)

-3/4

c)

3/5

d)

4/5

40.

Set up the problem so that you can solve for X.

a)

sin X = 41/28

b)

tan X = 41/28

c)

cos X = 28/41

d)

sin X = 28/41

41.

Let (12,-5) be a point on the terminal side of θ.

What is Cos ø?

a)

13/12

b)

12/13

c)

-5/13

d)

-5/12

42.

Solve for x. Round to the nearest tenth.

a)

9.5

b)

30.8

c)

3.1

43.

Factor 2x²+ 4x – 3x – 6 by grouping. Remember to look for Standard Form, then for common factors.

a)

(2x – 3)(x + 2)

b)

2x² + x - 6

c)

(2x + 3)(x - 2)

44.

Factor by grouping:

5n³-10n²+3n-6

a)

(5n²+3)(n-2)

b)

(5n³+3)(n-2)

c)

(5n²-3)(n-2)

d)

10n(n²-6)

45.

Factor out the GCF:
10x³ - 15x

a)

x(10x² - 15)

b)

5x(2x² - 3)

c)

5(2x³ - 3x)

d)

5x²(10x - 3)

46.

Factor:
x² - 5x - 14

a)

(x - 2)(x + 3)

b)

(x - 2)(x + 7)

c)

(x + 2)(x - 7)

d)

(x - 2)(x - 3)

47.

Factor:x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

48.

$60m^3p^3n+48mp^6-30mp^3n$

a)

$12p^3\left(10m^2n+8p^3-5n\right)$

b)

$6mp^3\left(10m^2n+8p^3-5n\right)$

c)

$6mp^3\left(10m^2np+8p^3-5n\right)$

49.

$6x^2y+30xy+42x$

a)

$6x\left(xy+5y+7\right)$

b)

$3x\left(xy+5y+7\right)$

c)

$3\left(xy+5y+7\right)$

50.

Factor completely: 3x²-36x+96

a)

(x-4)(x-8)

b)

3(x-4)(x-8)

c)

3(x+1)(x+32)

d)

3(x-2)(x+16)

51.

What are the factors of
25x² - 81?

a)

(5x - 9)(5x + 9)

b)

(5x - 9)(5x - 9)

c)

(5x + 9)(5x + 9)

d)

Cannot be factored

52.

Factor Completely.
8x³ - 18x

a)

2x(4x²-9)

b)

(4x²+3)(2x-3)

c)

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

d)

PRIME

53.

f(x) = x²+9
g(x) = x-9
Find f(x)-g(x).

a)

x²+x+9

b)

x²-x+9

c)

x²-x

d)

x²-x+18

54.

f(x)=x²+1
g(x)=2x-5
Find f(x)-g(x)

a)

x²-2x+6

b)

-x²+2x+4

c)

-x²-2x-6

d)

x²-2x-4

55.

f(x)=x³-3x
g(x)=-4x+1
Find f(x)*g(x)

a)

-4x³-5x²-3

b)

-4x³+2x²-3x

c)

-4x⁴+x³+12x²-3x

d)

-4x^4-x³+12x²⁺3x

56.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))

a)

19

b)

23

c)

-10

d)

None of these.

57.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(0))

a)

16

b)

4

c)

-4

d)

None of these.

58.

When f(x) = 2x and g(x) = x²+ 3 , find f(g(x)).

a)

x²+ 2x + 3

b)

4x²+ 3

c)

2x²+ 3

d)

2x²+ 6

59.

If f(x) = 2x and g(x) = 2x - 7, find f(x)/g(x).

a)

(2x - 7)/(2x)

b)

-7

c)

(2x)/(2x - 7)

d)

1x - 3.5

60.

f(g(3)) =

(a)

61.

f(h(-4)) =

(a)

62.

g(f(2)) =

(a)

63.

h(f(-2)) =

(a)

64.

Given the graph of f(x), evaluate f(2).

a)

undefined

b)

-1

c)

5

d)

2

65.

Given the graph of f(x), evaluate f(4).

(a)

66.

Given the graph of f(x), evaluate f(-1).

(a)

67.

Find h(5) using the equation.

a)

-25

b)

25

c)

3

d)

7

e)

undefined

68.

Find h(-10) using the equation.

a)

-100

b)

100

c)

3

d)

-8

e)

undefined

69.

Evaluate k(3) given the equation.

a)

0

b)

undefined

c)

6

70.

Does this graph have a minimum or maximum? What point?

a)

Minimum at (0, 0)

b)

Minimum at (0, 2)

c)

Maximum at (0, 0)

d)

Maximum at (0, 2)

71.

Does this graph have a minimum or maximum? What point?

a)

minimum at (-3, -5)

b)

minimum at (3, 5)

c)

maximum at (-3, -5)

d)

maximum at (3, 5)

72.

Select the correct graph for the following piecewise function.

a)

b)

c)

d)

73.

Match the piecewise function to its graph.

a)

b)

c)

d)

74.

a)

b)

c)

d)

75.

a)

b)

c)

d)

Precal Final Exam Review

Total questions: 75

Worksheet time: 3hrs 20mins

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