Free Printable 1- precalc. unit 1

1.

Is this mapping a function or not a function?

a)

Function

b)

Not a Function

2.

All of the x values or inputs are called what?

a)

Domain

b)

Range

c)

Relation

d)

Function

3.

Is the relation a function? Why.

a)

Yes, because the x-value 11 has two y-values pair with it.

b)

Yes, because each x-value has only one y-value paired with it.

c)

No, because the x-value 11 has two y-values pair with it.

d)

No, because each x-value has only one y-value paired with it.

4.

Which set of values is a function?

a)

(9,5) (10,5) (9,-5) (10,-5)

b)

(3,4) (4,-3) (7,4) (3, 8)

c)

(6,-5) (7, -3) (8, -1) (9, 1)

d)

(2, -2) (5, 9) (5, -7) (1, 4)

5.

For the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.

a)

D: {1, -3, -4,}
R: {0, 1, 2, -4}

b)

D:{0, 1, 2, -4}
R:{1, -3, -4}

c)

D:{0, 1, 2, 3, 4}
R:{1, -3, -4}

6.

Which ordered pair could you add to the following list of points to create a function? (3, 5) (4, 9) (2, 5)

a)

(3, 7)

b)

(4, 1)

c)

(1, 9)

d)

(2, 6)

7.

What is the range of the following relation:
(9, -2) (4, 3) ( 8, 10) ( -4, 8)

a)

-4, 4, 8, 9

b)

-2, 3, 8, 10

c)

(9, -2) ( 4, 3)

d)

(8, 10) (-4, 8)

8.

f(x) = 2x³ - 3x² + 4x -10

What is the degree of f(x)?

a)

3

b)

2

c)

1

d)

0

9.

What is the degree of the polynomial function
P(x)=3x⁴-7x²-2x⁷-x+4?

a)

4

b)

7

c)

2

d)

1

10.

A function with degree 3 is called

a)

constant

b)

cubic

c)

linear

d)

quadratic

11.

If f(x) = 4x³ + 5x² - 3, find f(-2).

a)

-415

b)

-15

c)

-55

d)

-615

12.

Is this a function:

(-1, 1), (-2, 2), (-3, 2), (-4, 1)?

a)

Yes

b)

No

13.

Simplify: (x - 5)²

a)

x² - 25

b)

x² + 25

c)

x² - 10x + 25

d)

x² - 5x - 25

14.

Identify the domain:

a)

{3, 4, 5, 6, 7}

b)

{3, 4, 5}

c)

{6, 7}

15.

Identify the range:

a)

{3, 4, 5, 6, 7}

b)

{3, 4, 5}

c)

{6, 7}

16.

Classify by degree of polynomial:
3x² – 8x + 1

a)

Constant

b)

Linear

c)

Quadratic

d)

Cubic

17.

Simplify the expression.
x³(2x²+3x)

a)

2x⁵+3x⁴

b)

2x⁶+3x³

c)

5x⁹

d)

5x

18.

Use Synthetic Substitution to find f(-2)
f(x) = 2x⁴ - 3x³ + 1

a)

A. f(-2) = 51

b)

B. f(-2) = 11

c)

C. f(-2) = 63

d)

D. f(-2) = 57

19.

A polynomial that contains 3 terms is called a ________________________.

a)

binomial

b)

monomial

c)

trinomial

d)

triomial

20.

What is the degree of the following function?
y = 25 - x²

a)

25

b)

1

c)

2

d)

-1

21.

For what intervals of x is f(x) positive?

a)

x<-2 and x>2

b)

-2<x<2

c)

x≤-2 and x≥2

d)

x≥-4

22.

For what intervals of x is f(x) decreasing?

a)

x≤0

b)

x≥0

c)

-2<x<2

d)

x>-2

23.

For what intervals of x is f(x) negative?

a)

-2<x<2

b)

-2≤x≤2

c)

x<-2 and x>2

d)

x≤-4

24.

What is the range of f(x)?

a)

y≥-4

b)

all real numbers

c)

x≥-4

25.

For what intervals of x is f(x) increasing?

a)

all values of x

b)

x>6

c)

x<6

d)

no values of x

26.

For what intervals of x is f(x) negative?

a)

x<6

b)

x>6

c)

x<3

d)

all values of x

27.

For what intervals of x does f(x) have a positive slope?

a)

all values of x

b)

x>6

c)

x<6

d)

no values of x

28.

For what intervals of x is f(x) decreasing?

a)

-1≤x≤4

b)

-1<x<4

c)

-7<x<2

d)

x≥0

29.

For what intervals of x does f(x) have a negative slope?

a)

-1<x<4

b)

-1≤x≤4

c)

x<-6 and x>4

d)

-6<x<-1

30.

For what intervals of x is f(x) constant?

a)

-6≤x≤-1

b)

-1≤x≤4

c)

x<-6 and x>4

d)

-6<x<-1

31.

For what intervals of x is f(x) positive?

a)

-7<x<2 and x>5

b)

-7<x<2

c)

x<-6 and x>4

d)

-6<x<-1

32.

What is the domain of f(x)?

a)

all real numbers

b)

-8≤x≤7

c)

-6<x<2

d)

-1<x<4

33.

What is the limits of the function when x approching a?

a)

Undefined

b)

2

c)

Does not exist

34.

What is the limits of the graph above when x approaching 0?

a)

0

b)

−∞

c)

Does not exist

35.

Which of the following is true?

a)

b)

c)

d)

36.

Which of the following best describes the continuity at x = 3?

a)

Continuous

b)

Removable Point Discontinuity

c)

Non-removable Infinite Discontinuity

d)

Non-removable Jump Discontinuity

37.

Which of the following best describes the continuity at x = -3?

a)

Continuous

b)

Removable Point Discontinuity

c)

Non-removable Infinite Discontinuity

d)

Non-removable Jump Discontinuity

38.

Describe the end behavior.

a)

f(x)→∞ as x→-∞ and f(x)→∞ as x→∞

b)

f(x)→-∞ as x→-∞ and f(x)→-∞ as x→∞

c)

f(x)→∞ as x→-∞ and f(x)→-∞ as x→∞

d)

f(x)→-∞ as x→-∞ and f(x)→∞ as x→∞

39.

Describe the end behavior.

a)

f(x)→-∞ as x→-∞ and f(x)→∞ as x→∞

b)

f(x)→∞ as x→-∞ and f(x)→-∞ as x→∞

c)

f(x)→-∞ as x→-∞ and f(x)→-∞ as x→∞

d)

f(x)→∞ as x→-∞ and f(x)→∞ as x→∞

40.

Based on the graph, identify where the discontinuities are located.

(Select all that apply.)

a)

x = -4

b)

x = 2

c)

x = -1

d)

x = 4

41.

Which of the following is the end behavior of the following graph?

a)

$\lim_{x\rightarrow\infty}f\left(x\right)=\infty\$ and

$\lim_{x\rightarrow-\infty}f\left(x\right)=\infty\$

b)

$\lim_{x\rightarrow\infty}f\left(x\right)=\infty\$ and $\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty\$

c)

$\lim_{x\rightarrow\infty}f\left(x\right)=-\infty\$

and $\lim_{x\rightarrow-\infty}f\left(x\right)=\infty\$

d)

$\lim_{x\rightarrow\infty}f\left(x\right)=-\infty\$

and $\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty\$

42.

If $\lim_{x\rightarrow a}\ f\left(x\right)\$ does not exist, then $f\left(x\right)$ is undefined at the point $x=a.$

a)

True

b)

False

c)

cannot be determined

43.

Suppose h is a continuous function containing the ordered pairs shown in the table. On which interval must h have a zero?

a)

(12.163, 12.164)

b)

(12.164, 12.165)

c)

(12.165, 12.166)

d)

(12.166, 12.168)

44.

Describe the end behavior of the graph.

a)

$\lim_{x\rightarrow\infty}f\left(x\right)=\infty$

and

$\lim_{x\rightarrow-\infty}f\left(x\right)=\infty$

b)

$\lim_{x\rightarrow\infty}f\left(x\right)=\infty$

and $\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty$

c)

$\lim_{x\rightarrow\infty}f\left(x\right)=-\infty$ and

$\lim_{x\rightarrow-\infty}f\left(x\right)=\infty$

d)

$\lim_{x\rightarrow\infty}f\left(x\right)=-\infty$ and $\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty$

45.

Determine whether $f\left(x\right)=\frac{x^2+5x-6}{x-1}$ is continuous or discontinuous at $x=1.$

a)

continuous

b)

discontinuous, removable

c)

discontinuous, jump

d)

discontinuous, essential

46.

A function $f\left(x\right)$ has to be continuous at $x=a$ if the $\lim_{x\rightarrow a}\ f\left(x\right)$ exists.

a)

True

b)

False

c)

cannot be determined

47.

The function $h\left(t\right)=\left\{_{t+6,\ t\ge-2}^{t^{2,\ \ t<-2}}\ \right\}$ is continuous at t = -2.

a)

True

b)

False

48.

Determine whether the function f(x) is continuous or discontinuous at $x=2.$

a)

continuous

b)

discontinuous, essential

c)

discontinuous, removable

d)

discontinuous, jump

49.

Assume f(x) is continuous over the interval [-2, 3]. The function f has at least how many zeros?

a)

1

b)

2

c)

3

d)

4

50.

Describe the end behavior of the graph.

a)

$\lim_{x\rightarrow\infty}f\left(x\right)=\infty$

and

$\lim_{x\rightarrow-\infty}f\left(x\right)=\infty$

b)

$\lim_{x\rightarrow\infty}f\left(x\right)=\infty$

and $\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty$

c)

$\lim_{x\rightarrow\infty}f\left(x\right)=-\infty$ and

$\lim_{x\rightarrow-\infty}f\left(x\right)=\infty$

d)

$\lim_{x\rightarrow\infty}f\left(x\right)=-\infty$ and $\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty$

51.

What is a possible point of discontinuity for the function $f\left(x\right)=\ \frac{x^2-25}{x+5}$ ?

a)

none

b)

5

c)

-5

d)

0

52.

Suppose t is a continuous function containing the ordered pairs shown in the table. On which interval(s) must t attain a value of -2.5? Select all that apply.

a)

(1, 2)

b)

(2, 3)

c)

(3, 4)

d)

(4, 5)

e)

(5, 6)

53.

Given the function f(x) = x³ + x - 3, which of the intervals below contains a zero?

a)

[-1,1]

b)

[0,1]

c)

[1,2]

d)

None of these intervals

54.

f(x) = 2x² + 12x + 16
What is the average rate of change of f(x) on the interval [-3, -2].

a)

2

b)

1/2

c)

-2

d)

-1/2

55.

What was the average rate of change in the population from 1900 to 1990?

a)

175 million people/year

b)

1.94 million people/year

c)

2.13 million people/year

d)

-1 million people/year

56.

Approximate the instantaneous rate of change of the function at x = -1.

f\left(x\right)=3x^2+2x-1

a)

-4

b)

-1/4

c)

3

d)

-2

57.

Find the instantaneous rate of change for f(x) at x = 2 for $f\left(x\right)\ =-\frac{3}{4}x^4+2$

a)

-24

b)

- $\frac{3}{2}$

c)

24

d)

- $\frac{3}{4}$

58.

Find the instantaneous rate of change

a)

88.25

b)

39.5

c)

87.75

d)

88.5

59.

If the position of a particle is represented by s(t) = t² + 2, what is its instantaneous velocity at t = 3?

a)

5 ft/sec

b)

6 ft/sec

c)

3 ft/sec

d)

4 ft/sec

60.

f(x) = 3x² + 12x + 16

Estimate the instantaneous rate of change at x = -1.

a)

About 6

b)

About -6

c)

About 0

d)

About 5

61.

Speed

a)

when a distance l is traveled during a time interval Δt is

b)

the time derivative of the displacement (a limit as the time interval approaches Zero)

c)

is the absolute value of the velocity vector. For a moving object, speed is always positive.

d)

finding the rate of change of a function with respect to one of its variables

62.

Which of the following are ways to find the rate of change?

a)

change in y over change in x

b)

rise over run

c)

subtract y coordinates over subtract x coordinates

d)

all of the above

63.

Which of the following are ways to find the rate of change?

a)

change in y over change in x

b)

rise over run

c)

subtract y coordinates over subtract x coordinates

d)

all of the above

64.

Find the average rate of change of f(x)=2x²+3x-1 from 1 to 2.

a)

18

b)

-9

c)

9

d)

3

65.

Whats is the average rate of change of the function $f\left(x\right)\ =\ -x^2+\ 1\ at\ the\ interval\ x\ =\ -2\ and\ x\ =\ 1?$

(a)

66.

Whats is the average rate of change of the function $f\left(x\right)\ =\ 2x^2+\ 1\ at\ the\ interval\ x\ =\ 0\ and\ x\ =\ 1?$

(a)

67.

What is the average rate of change of the function $f\left(x\right)\ =\ -\frac{1}{x+2}\ at\ the\ interval\ x\ =\ 0\ and\ x\ =\ 1?$ Input in simplified fraction form.

(a)

68.

Given the table. Find the average rate of change from the interval x = 0 to x = 4.

(a)

69.

Given the table. Find the average rate of change from the interval x = 1 to x = 3.

(a)

70.

Given the table. Find the average rate of change from the interval x = 1 to x = 2.

(a)

71.

Given the graph, find the average rate of change from x = -1 to x = 2.

(a)

72.

Given the graph, find the average rate of change from x = 1 to x = 3.

(a)

73.

Find the average rate of change.

a)

2 sec/feet

b)

2 feet/sec

c)

2 feet

d)

2 sec

74.

After 30 baseball games, Marco had 25 hits. If after 100 games he had 80 hits, what is Marco's average hits per baseball game?

a)

0.79 hits/game

b)

1.25 hits /game

c)

2.25 hits / game

d)

0.62 hits/game

75.

Find the slope of the line passing through (19, -16) , (-7, -15) in reduced form.

(a)

76.

Find the slope of the line passing through (1, -19) , (-2, -7) in reduced form.

(a)

77.

Find the slope of the line passing through (19, 3) , (20, 3) in reduced form.

(a)

78.

Find the slope of the line passing through (6, -12) , (15, -3) in reduced form.

(a)

79.

During the year 2000, the price of gold was $279.29 per ounce. By 2022 the price jumped to $1868.8 per ounce. What is the average rate of change in the price of gold from 2000 to 2022? Round your answer to the nearest dollar and input without a dollar sign.

(a)

80.

Slopes of vertical lines are undefined?

a)

Always True

b)

Sometimes True

c)

Never True

81.

Slopes of horizontal lines are negative?

a)

Always True

b)

Sometimes True

c)

Never True

82.

This line has a positive slope.

a)

Sometimes True

b)

Always True

c)

Never True

83.

This line has a positive slope.

a)

Always True

b)

Sometimes True

c)

Never True

84.

Find the Average Rate of Change from the intervals: $x\ =\ \pi\ and\ x\ =\ \frac{3\pi}{2}.$

a)

$\frac{2}{\pi}$

b)

$\frac{\pi}{2}$

c)

$\pi$

d)

$2\pi$

1- precalc. unit 1

Total questions: 84

Worksheet time: 3hrs 2mins

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