Free Printable Review Day 1

1.

Which statement correctly describes the composition (f ∘ g)(x)?

a)

Add f(x) and g(x) then simplify

b)

Apply f first, then apply g to the result

c)

Apply g first, then apply f to the result

d)

Multiply f(x) and g(x) together

2.

Let k(x) = |x − 3|. What is k(10)?

a)

7

b)

−7

c)

13

d)

3

3.

Given p(x) = √(5 − x), what is the domain of p?

a)

x ≤ 5

b)

x ≥ 5

c)

x < 5

d)

x > 5

4.

Let f(x) = 3x − 1 and g(x) = x + 4. What is (f ∘ g)(2)?

a)

9

b)

13

c)

15

d)

11

5.

Let f(x) = 3x − 1 and g(x) = x + 4. What is (g ∘ f)(2)?

a)

7

b)

13

c)

9

d)

11

6.

Let f(x) = $x^2 - 7$ and g(x) = $2x + 1$ . Which expression equals $(f \circ g)(x)$ ?

a)

$4x^2 + 4x - 12$

b)

$4x^2 + 4x - 8$

c)

$4x^2 + 4x - 10$

d)

$4x^2 + 4x - 6$

7.

In the strategy, which function corresponds to the inside expression?

a)

g(x) because it is inserted into f

b)

f(x) because it modifies x directly

c)

h(x) because it is the composition

d)

Neither because both are outer

8.

Which function acts on the input after the inner expression is formed?

a)

x, the identity function that acts always

b)

f(x), the outer function that acts last

c)

g(x), the inner function that acts last

d)

h(x), the original function that acts first

9.

Which cue most reliably reveals the inner function in a complicated expression?

a)

A subexpression substituted into another rule

b)

Any constant term appearing in the function

c)

The variable with the highest exponent shown

d)

The expression outside all parentheses

10.

Choose a valid decomposition for h(x)=|3x+2|.

a)

g(x)=x+2, f(u)=|3u|

b)

g(x)=3x+2, f(u)=|u|

c)

g(x)=|x|, f(u)=3u+2

d)

g(x)=3x, f(u)=|u|+2

11.

Choose f and g so that h(x)=1/√(3x+1).

a)

g(x)=3x, f(u)=1/√(u+1)

b)

g(x)=√x, f(u)=1/(3u+1)

c)

g(x)=3x+1, f(u)=1/√u

d)

g(x)=1/(3x+1), f(u)=√u

12.

Which is a correct inner function candidate for $cos(5x^2−6)$ ?

a)

$g(x)=x^2−6$

b)

g(x)=5x−6

c)

g(x)=cos x

d)

$g(x)=5x^2−6$

13.

Which option best explains why order matters in compositions?

a)

Applying functions in reverse usually gives a different result

b)

Applying functions in any order gives identical outputs

c)

The outer function always cancels the inner function

d)

The inner function is always a linear expression

14.

For f(x) = √(x − 2) and g(x) = 4x + 1, write (f ∘ g)(x) and state its domain.

a)

√(4x + 1 − 2), x > 1/4

b)

√(4x − 1), x ≥ 1/4

c)

√(4x + 1 − 2), x ≥ 1/4

d)

√(4x − 2), x ≥ 1/2

15.

Given f(x) = 1/x and g(x) = x − 7, find (f ∘ g)(x) and state its domain.

a)

x/(x − 7), x ≠ 0

b)

1/(x + 7), x ≠ −7

c)

1/(x − 7), x > 7

d)

1/(x − 7), x ≠ 7

16.

Write h(x) = √(3x + 2) as a composition f(g(x)). Choose f and g.

a)

g(x)=3x+2, f(u)=√u

b)

g(x)=√x, f(u)=3u+2

c)

$g(x)=x^2$ , $f(u)=\sqrt{3u+2}$

d)

g(x)=3x, f(u)=√(u+2)

17.

Given f(x) = $ln x$ and g(x) = $e^{2x}$ , evaluate (f ∘ g)(0).

a)

ln 2

b)

1

c)

2

d)

0

18.

If f(x)= $2x-1$ and g(x)= $x^2+4$ , compute (g ∘ f)(3).

a)

50

b)

44

c)

40

d)

34

19.

Given f(x)=1/x and g(x)=x−7, which x makes (f ∘ g)(x) undefined?

a)

x=1

b)

x=0

c)

x=7

d)

x=−7

20.

For f(x)= $x^2−4x$ and g(x)= $√x$ , which interval is excluded from the domain of (g ∘ f)(x)?

a)

(4,∞)

b)

No interval

c)

(0,4)

d)

(−∞,0)

21.

Which of the following words can be used to identify "x"

Choose 3

a)

Domain

b)

Range

c)

Input

d)

Output

e)

Independent

22.

Find the range of the function below given the domain

$f\left(x\right)=3x+2\ \ D:\ x=\left\{-2,0,2\right\}$

a)

{4, 2, -8}

b)

$\left\{-4,\ 2,\ 8\right\}$

c)

$\left\{-4,\ -2,\ -8\right\}$

d)

{-8, 8, 2}

23.

What is the domain of the graph?

a)

y≥1

b)

x ≥ 1

c)

All real numbers

d)

none of these

24.

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)

25.

Is this graph a function or not a function?

a)

Function

b)

Not a Function

26.

Give the domain and range. Tell if it is a function.

a)

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

b)

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

c)

D: {-4, -2, 0, 2}
R: {-2, -2, 1, 1}
Not a Function

d)

D: {-4, -2, 0, 2}
R: {-2, 1}
Not a Function

27.

.

a)

Function

b)

Not a Function

28.

Let w(x) = 3x - 7. If w(x) = 14, find x.

a)

7

b)

35

c)

2.33333

d)

-49

29.

a)

Function

b)

Not a Function

30.

Is this graph a function or not a function?

a)

Function

b)

Not a Function

31.

What are the extrema of the graph?

a)

Max = (0,-4)

Min = (-1.5,0) and (1.5, 0)

b)

Max = (0,1.5) and (0, -1.5)

Min = (-4,0)

c)

Max = (-1.5,0) and (1.5, 0)

Min = (0,-4)

d)

Max = (-4,0)

Min =(0,1.5) and (0, -1.5)

32.

What are the extrema of the graph?

a)

Max = (2, -3), (1, 2)

Min = (-3, -1), (-1, 4)

b)

Max = (-3, -1), (-1, 4)

Min = (2, -3), (1, 2)

c)

Max = (-1, -3), (4, -1)

Min = (-3, 2), (2, 1)

d)

Max = (-3, 2), (2, 1)

Min = (-1, -3), (4, -1)

33.

How many extrema are there in this graph?

a)

2 max, 2 min

b)

3 max, 2 min

c)

2 man, 3 min

d)

3 increasing intervals, 2 decreasing intervals

e)

2 increasing intervals, 3 decreasing intervals

34.

How many extrema are there in this graph?

a)

2 max, 2 min

b)

3 max, 2 min

c)

2 man, 3 min

d)

3 increasing intervals, 2 decreasing intervals

e)

2 increasing intervals, 3 decreasing intervals

35.

How many increasing and decreasing intervals are there in this graph?

a)

2 increasing, 2 decreasing

b)

1 increasing, 2 decreasing

c)

2 increasing, 1 decreasing

d)

1 increasing, 1 decreasing

36.

What are the increasing intervals?

a)

(- ∞, 0) & (2, ∞ )

b)

(-1, 0) & (2,4)

c)

(0,2) & (-3, -7)

d)

(-8, -3) & (-7, 8)

37.

What are the decreasing intervals on the graph?

a)

(-∞, 0) & (-4, ∞)

b)

(-∞, -1) & (1, ∞)

c)

(-∞, -2) & (2, ∞)

d)

(-∞, 0) & (4, ∞)

38.

What is/are the increasing interval(s) for the function shown?

a)

$\left(-3,\ 1\right)$

b)

$\left(4,\ 8\right)$

c)

$\left(-\infty,1\right)\ and\ \left(-3,\ 1\right)$

39.

What is the range?

a)

$\left[-7,6\right]$

b)

$\left(-\infty,6\right)$

c)

$\left(-8,2\right)$

d)

\left(-\infty,2\right)

40.

Which one of the following functions is even?

a)

f(x) = x⁴ + x³

b)

g(x) = x⁴ + x²

c)

h(x) = x⁵ + x³

d)

k(x) = x³ + x

41.

Which one of the following functions is odd?

a)

f(x) = 3x⁴ - 4x³

b)

g(x) = 5x⁴ + 3x²

c)

h(x) = 6x⁵ - x³

d)

k(x) = x⁶ + 8x²

42.

The function shown in the graph is:

a)

even

b)

odd

c)

neither even nor odd

d)

both even and odd

43.

The function in the graph is:

a)

even

b)

odd

c)

neither even nor odd

d)

both even and odd

44.

The function shown in the graph is:

a)

even

b)

odd

c)

neither odd nor even

d)

both odd and even

45.

Which one of the following functions is odd?

a)

f(x) = 3x⁴ - 4x³

b)

g(x) = 5x⁴ + 3x²

c)

h(x) = 6x⁵ - x³

d)

k(x) = x⁶ + 8x²

46.

Which one of the following functions is neither even or odd?

a)

f(x) = x⁴ + x³

b)

g(x) = x⁴ + x²

c)

h(x) = x⁵ + x³

d)

k(x) = x³ + x

47.

Is the graph an even, odd, or neither function.

a)

Even

b)

Odd

c)

Neither

48.

Is the graph an even, odd, or neither function?

a)

Even

b)

Odd

c)

Neither

49.

Is the graph an even, odd, or neither function

a)

Even

b)

Odd

c)

Neither

50.

Is the graph an even, odd, or neither function
f(x)=x³-x²

a)

even

b)

odd

c)

neither

51.

Is the graph an even, odd, or neither function?

a)

Even

b)

Odd

c)

Neither

52.

Is the graph an even, odd, or neither function?

a)

Even

b)

Odd

c)

Neither

53.

Is this function even, odd or neither?

a)

Even

b)

Odd

c)

Neither

54.

a)

Even Function

b)

Odd Function

c)

Function - Neither Even Nor Odd

d)

Both Even and Odd Function

e)

Not a Function

55.

a)

Even Function

b)

Odd Function

c)

Function - Neither Even Nor Odd

d)

Not a Function

56.

Which of the following is an even function (choose all that apply)?

a)

$\left\{\left(-2,5\right)\left(-1,9\right)\left(2,5\right)\left(1,9\right)\right\}$

b)

$\left\{\left(3,8\right)\left(5,1\right)\left(-3,-8\right)\left(-5,1\right)\right\}$

c)

$\left\{\left(0,0\right)\left(1,1\right)\left(2,4\right)\left(3,9\right)\left(4,16\right)\right\}$

d)

$\left\{\left(7,4\right)\left(5,5\right)\left(0,2\right)\left(-5,5\right)\left(-7,4\right)\right\}$

e)

$\left\{\left(0,3\right)\left(0,8\right)\left(0,-1\right)\left(0,-12\right)\right\}$

57.

Which table definitely represents an odd function?

a)

b)

c)

d)

58.

What is Mrs. Gordon's rate from 0 to 2 seconds?

a)

2.5 feet per second

b)

.4 feet per second

c)

5 feet per second

d)

.2 feet per second

59.

Calculate the average rate of change from 20 to 40 minutes.

a)

-2 minutes per gallon

b)

-20 minutes per gallon

c)

-2 gallons per minute

d)

-20 gallons per minute

60.

Find the average rate of change over the given interval.

a)

4

b)

7

c)

7/3

d)

3/7

61.

A climber is on a hike. After 2 hours he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 700 feet. What is the average rate of change?

a)

200

b)

150

c)

300

d)

75

62.

What is the average rate of change from x=0 to x=1

a)

-3

b)

3

c)

0

d)

2

Review Day 1

Total questions: 62

Worksheet time: 5hrs 21mins

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