Deck 2: Functions and Their Graphs

Question 1

Suppose that f and g are the functions defined by the tables below. What is the domain of f ?

Answer 1

{1, 2, 3, 4}

Question 2

Suppose that f and g are the functions defined by the tables below. What is the domain of g?

A) {3, 4, 5, 6}
B) {5, 6, 7, 8}
C) {1, 2, 3, 7}
D) {2, 3, 4, 6}

Answer 2

{5, 6, 7, 8}

Question 3

Suppose that f and g are the functions defined by the tables below. What is the range of f ?

Answer 3

{3, 4, 5, 6}

Question 4

Suppose that f is the function defined by the table below. The number 6 is in the domain of f.

Question 5

Suppose that f and g are the functions defined by the tables below. What is the range of g?

A) {8, 9, 10, 11}
B) {9, 10, 11, 12}
C) {10, 11, 12, 13}
D) {7, 8, 9, 10}

Question 6

Suppose that f is the function defined by the table below. Give the table of values of f ^-1.

Question 7

Suppose that g is the function defined by the table below. The number 7 is in the domain of $g^{-1}$ .

Question 8

Suppose that f is the function defined by the table below. What is the domain of f ^-1?

A) {8, 9, 10, 11}
B) $\left\{\frac{1}{8}, \frac{1}{9}, \frac{1}{10}, \frac{1}{11}\right\}$
C) {10, 11, 12, 13}
D) {8, 10, 12, 14}

Question 9

Suppose that g is the function defined by the table below. What is the range of g ^-1?

Question 10

If the function f is given by the following table, then $f^{ -1}$ can be represented by the adjacent graph.

Question 11

Sketch the graph of g ^-1, where g is the function defined by the table below.

A)

B)

C)

D)

Question 12

If f is defined by the first table of values, then $\left(f \circ f^{-1}\right)$ is defined for the last table of values, regardless the value of k.

Question 13

Suppose that f and g are the functions defined by the tables below. Give the table of values of $g \circ f$
.

Question 14

Suppose that f and g are the functions defined by the tables below. Give the table of values of $(f \circ g)^{-1}$
.

Question 15

Consider the function f with domain [0, 12] whose graph is shown below.

A) What is the largest interval contained in the domain of f on which f is increasing?
B) Let g denote the function obtained from f by restricting the domain to the interval in part (a). What is the domain of g ^-1 ?

Question 16

Consider the function f with domain [0, 12] whose graph is shown below.

A) What is the largest interval contained in the domain of f on which f is decreasing?
B) Let h denote the function obtained from f by restricting the domain to the interval in part (a). What is the range of h ^-1 ?

Question 17

Consider the function f with domain (0, 20] whose graph is shown below, where a = 4, b = 12, and c = 20. Find the largest interval where f is increasing.

A) (0, 4]
B) (12, 20)
C) [8, 20]
D) [12, 20]

Question 18

Consider the function f whose graph is shown below. Find the interval(s) where the function is decreasing. Here, a = -8, b = -4, c = 6, and d = 20.

Question 19

Every odd function is one-to-one.

Question 20

The sum of two decreasing functions is decreasing.

Question 21

Consider the function f whose graph is shown below. Use the horizontal line test to determine if the function has an inverse.

Question 22

Consider the function f whose graph is shown below. Sketch the graph of the inverse.

Question 23

Suppose f(x) = 9x + 1. Evaluate f ^-1(10).

Question 24

Suppose f(x) = -x - 16. Evaluate f ^-1(-11).

A) 16
B) 14
C) -5
D) 15

Question 25

Suppose $f(x)=\frac{x+10}{x+9}$ . Evaluate f ^-1(2).

Question 26

Suppose $f(x)=\frac{x-14}{x-15}$
. Evaluate f ^-1(14).

Question 27

Suppose f(x) = 43x + 1. Find a formula for f ^-1.

Question 28

Suppose f(x) = 2x + 7. Find a formula for f ^-1.

Question 29

Suppose $f(x)=4+\frac{x-4}{x+4}$ . Evaluate f ^-1(4).

A) 4
B) 5
C) 3
D) -4

Question 30

Suppose $f(x)=-11-\frac{x-2}{x-1}$ . Evaluate f ^-1(-11).

Question 31

Suppose h(x) = -11 + x², where the domain of h is the set of positive numbers. Find a formula for h^-1.

Question 32

Suppose h(x) = -6 - 2x², where the domain of h is the set of positive numbers. Find a formula for h^-1.

Question 33

Suppose $f(x)=\frac{1}{2 x-5}$ . Find the domain of f.

Question 34

Suppose $f(x)=\frac{x-8}{x+8}$ . Find the domain of f ^-1.

Question 35

Suppose $f(x)=39+\frac{x+39}{x-39}$ . Find the range of f ^-1.

Question 36

Suppose $f(x)=34+\frac{1}{x+34}$ . Find the range of f.

A) $\{x: x \neq 68\}$
B) $\{x: x \neq-34\}$
C) $\{x: x \neq-68\}$
D) $\{x: x \neq 34\}$

Question 37

Suppose f(x) = x² + 20, where the domain of f equals
$(0, \infty)$ . Find the range of f.

Question 38

Suppose f(x) = 2 - 16x², where the domain of f equals $(0, \infty)$ . Find the domain of f ^-1.

Question 39

Suppose f(x) = x⁵ + 17x³. Which of the following alternatives equals $f^{-1}\left(\frac{69}{32}\right)$ ?

A) 1
B) $\frac{17}{18}$
C) $\frac{1}{2}$
D) $\frac{18}{17}$

Question 40

Suppose f(x) = 5x³ + x. Which of the following alternatives equals f ^-1(630)?

A) 5
B) $\frac{25}{6}$
C) 6
D) $\frac{26}{5}$

Question 41

Suppose f(x) = x⁷ + x⁵. Evaluate (f ^-1(13))⁷ + (f ^-1(13))⁵ + 13.

Question 42

Suppose f(x) = x⁷ + 2x³. Evaluate (f ^-1(12))⁷ + 2(f ^-1(12))³ + 1.

Question 43

Suppose $f(x)=15 x+8$ and $g(x)=\frac{x-8}{15}$ . Evaluate $(f \circ g)(x)$ .

Question 44

Suppose $f(x)=x^{2}+11$ and $g(x)=\sqrt{x-11}$ . Evaluate $(f \circ g)(x)$ .

Question 45

Suppose $f(x)=12 x+6$ And $g(x)=\frac{x-6}{12}$ . Then which must be true?

A) $(f \circ g)(x)>(g \circ f)(x)$
B) $(f \circ g)(x)<(g \circ f)(x)$
C) $(f \circ g)(x)=(g \circ f)(x)$
D) Impossible to determine

Question 46

Suppose $f(x)=x^{2}+10$ and $g(x) = \sqrt{x-10}$ . Determine if f and g are inverses.

Question 47

Suppose $f(x)=10 x+2$ and $g(x) = \frac{x-3}{10}$ . Determine if f and g are inverses.

Question 48

Suppose $f(x)=9 x^{4}+6$ on the domain $(-\infty, \infty)$ Determine if f has an inverse.

Question 49

Assuming that f and g are the functions completely defined by the tables below, evaluate the expression $(f \circ g)(4)$
.

Question 50

Assuming that g is the function completely defined by the table below, evaluate the expression $(g \circ g)(4)$ .

Question 51

Assuming that f and g are the functions completely defined by the tables below, evaluate the expression $(g \circ f)(4)$
.

Question 52

Assuming that f is the function completely defined by the table below, evaluate the expression $(f \circ f)(1)$ .

A) 2
B) 1
C) 0
D) 3

Question 53

Evaluate $(f \circ g)(14)$ assuming that $f(x)=\sqrt{x+1}$ and $g(x)=\frac{x}{x+1}$ .

Question 54

Evaluate $(f \circ h)(-13)$ assuming that $f(x)=\sqrt{x+1}$ and $h(x)=|x+2|$ .

Question 55

Evaluate $(g \circ h)(-19)$ Assuming that $g(x)=\frac{x}{x+1}$ And $h(x)=|x+2|$ .

A) $\frac{17}{18}$
B) $-\frac{17}{18}$
C) $\frac{18}{17}$
D) $-\frac{18}{17}$

Question 56

Evaluate $(h \circ f)(20)$ assuming that $f(x)=\sqrt{x+1}$ and $h(x)=|x+2|$ .

Question 57

Suppose $h(x)=\left(\frac{x-9}{x+9}+9\right)^{2}$ . If f(x) = (x + 9)², then find a function g such that $h=f \circ g$ .

Question 58

Suppose $h(x)=\sqrt{6-\frac{6}{x^{2}+36}}$ . If $f(x)=\sqrt{6-x}$ , then find a function g such that $h=f \circ g$ .

Question 59

Suppose $h(x)=8+\sqrt{\frac{8}{x^{2}+64}}$ . If $g(x)=\frac{8}{x^{2}+64}$ , then find a function f such that $h=f \circ g$ .

A) $f(x)=8-x^{2}$
B) $f(x)=8+\sqrt{x}$
C) $f(x)=8-x$
D) $f(x)=\sqrt{x}-8$

Question 60

Suppose $h(x)=3+\sqrt{\frac{3}{x^{2}+9}}$ . If $g(x)=x^{2}$ , then find a function f such that $h=f \circ g$ .

Question 61

Suppose $h(x)=\left(\frac{x^{2}}{x^{2}+36}-1\right)^{2}$ . If $g(x)=\frac{x^{2}}{x^{2}+36}$ , then find a function f such that $h=f \circ g$ .

Question 62

For $f(x)=x^{2}+4$ And $g(x)=\frac{2}{x}$ , find a formula for $g \circ f$ . Simplify your results as much as possible.

A) $-\frac{4}{x^{2}+4}$
B) $-\frac{2}{x^{2}+4}$
C) $\frac{2}{x^{2}+4}$
D) $\frac{4}{x^{2}+4}$

Question 63

For $f(x)=\frac{14 x}{14 x+13}$ and $g(x)=\frac{13 x}{14-14 x}$ , find a formula for $g \circ f$ . Simplify your results as much as possible.

Question 64

For $f(x)=\frac{26}{26+x}$ and $g(x)=\frac{x-1}{x+1}$ , find a formula for $g \circ f$ . Simplify your results as much as possible.

Question 65

if $f(x)=7\sqrt{x} and g(x)=\frac{x^2}{49}$ then f(g(x)) = g(f(x)) for each x > 0.

Question 66

Find a number b such that $f \circ g=g \circ f$ , where $f(x)=5 x+b$ and $g(x)=2 x+5$ .

Question 67

Find a number c such that $f \circ g=g \circ f$ , where $f(x)=15 x+1$ $g(x)=c x-15$ .

A) 241
B) -239
C) -209
D) -210

Question 68

If f(x) = 6x + b and g(x) = 6x + c, then f $\circ$ g = g $\circ$ f if and only if b = c.

Question 69

For $f(x)=4 x+6$ and $g(x)=7 x-7$ , find a formula for $(f+g)$ . Simplify your results as much as possible.

Question 70

For $f(x)=2 x+7$ and $g(x)=8 x-11$ , find a formula for $(f-g)$ . Simplify your results as much as possible.

Question 71

For $f(x)=5 x^{2}+4$ and $g(x)=2 x-5$ , find a formula for $(f+g)$
. Simplify your results as much as possible.

Question 72

For $f(x)=4 x+4$ and $g(x)=3 x$ , find a formula for $(f \times g)$ . Simplify your results as much as possible.

Question 73

For $f(x)=28 x^{2}+35 x$ and $g(x)=7 x$ , find a formula for $(f / g)$ . Simplify your results as much as possible.

Question 74

For $f(x)=3 x+3$ and $g(x)=2 x+5$ , find a formula for $(f \times g)$ . Simplify your results as much as possible.

Question 75

For $f(x)=6 x^{2}+17 x+5$ and $g(x)=3 x+1$ , find a formula $(f / g)$ . Simplify your results as much as possible.

Question 76

Choose the composite of functions that would create the graph:

A) $(f \circ g)(x)$ For $f(x)=x^{2}$ And $g(x)=x+5$
B) $(g \circ f)(x)$ For $f(x)=x^{2}$ And $g(x)=x-5$
C) $(g \circ f)(x)$ For $f(x)=x^{2}$ And $g(x)=x+5$
D) $(f \circ g)(x)$ For $f(x)=x^{2}$ And $g(x)=x-5$

Question 77

Choose the composite of functions that would create the graph:

A) $(f \circ g)(x)$ For $f(x)=x^{2}$ And $g(x)=x+6$
B) $(g \circ f)(x)$ For $(g \circ f)(x)$ And $g(x)=x-6$
C) $(g \circ f)(x)$ For $f(x)=x^{2}$ And $g(x)=x+6$
D) $(f \circ g)(x)$ For $f(x)=x^{2}$ And $g(x)=x-6$

Question 78

Choose the composite of functions that would create the graph:

A) $(g \circ f)(x)$ For $f(x)=x^{2}$ And $g(x)=-(x-3)$
B) $(g \circ f)(x)$ For $f(x)=-x^{2}$ And $g(x)=x-3$
C) $(g \circ f)(x)$ For $f(x)=-x^{2}$ And $g(x)=x+3$
D) $(f \circ g)(x)$ For $f(x)=x^{2}$ And $g(x)=x-3$

Question 79

Choose the composite of functions that would create the graph:

A) $(f \circ g)(x)$ For $f(x)=x^{2}$ And $g(x)=x+6$
B) $(g \circ f)(x)$ For $f(x)=x^{2}$ And $g(x)=x-6$
C) $(g \circ f)(x)$ For $f(x)=x^{2}$ And $g(x)=x+6$
D) $(f \circ g)(x)$ For $f(x)=x^{2}$ And $g(x)=x-6$

Question 80

Choose the composite of functions that would create the graph:

A) $(f \circ g)(x)$ For $f(x)=x^{2}$ And $g(x)=x+7$
B) $(g \circ f)(x)$ For $f(x)=x^{2}$ And $g(x)=x-7$
C) $(g \circ f)(x)$ For $f(x)=x^{2}$ And $g(x)=x+7$
D) $(f \circ g)(x)$ For $f(x)=x^{2}$ And $g(x)=x-7$