Deck 3: Functions and Graphs

Question 1

Determine whether the following rule defines $y$ as a function of $x$ .

-The $x$ , y pairs: $\{(-1,1),(2,8),(4,2),(9,-8),(11,-3)\}$

Answer 1

True

Question 2

Determine whether the following rule defines $y$ as a function of $x$ .

-The $x$ , y pairs: $\{(-7,-5),(-7,-3),(-1,1),(6,-7),(7,5)\}$

Answer 2

False

Question 3

Determine whether the following rule defines $y$ as a function of $x$ .

-The $x$ , y pairs: $\{(2,-7),(2,9),(4,-6),(8,-8),(12,3)\}$

Answer 3

False

Question 4

Determine whether the following rule defines $y$ as a function of $x$ .

- $y=\sqrt{6 x-3}$

Question 5

Determine whether the following rule defines $y$ as a function of $x$ .

- $x=y^{2}$

Question 6

Determine whether the following rule defines $y$ as a function of $x$ .

- $x=|y-3|$

Question 7

Determine whether the following rule defines $y$ as a function of $x$ .

- $y=|x-3|$

Question 8

Determine whether the following rule defines $y$ as a function of $x$ .

- $y=\frac{9 x}{5 x-2}$

Question 9

State the domain of the given function.

- $f(x)=-5 x+3$

A) all real numbers except 0
B) $(-\infty, 0]$
C) $[0, \infty)$
D) $(-\infty, \infty)$

Question 10

State the domain of the given function.

- $y=\sqrt{15-x}$

A) $[15, \infty)$
B) $(-\infty, \infty)$
C) $(-\infty, 15)$
D) $(-\infty, 15]$

Question 11

State the domain of the given function.

- $y=\frac{x}{x-7}$

A) all real numbers except 7
B) 7
C) $(-\infty, \infty)$
D) $(7, \infty)$

Question 12

State the domain of the given function.

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

A) all real numbers except 6
B) all real numbers except -6
C) $(-6, \infty)$
D) $(-\infty, \infty)$

Question 13

State the domain of the given function.

- $f(x)=|8 x+4|$

A) all real number except $-\frac{1}{2}$
B) $[0, \infty)$
C) $\left[-\frac{1}{2}, \infty\right)$
D) $(-\infty, \infty)$

Question 14

State the domain of the given function.

- $f(x)=\sqrt{x+2}$

A) all real numbers except -2
B) $(-2, \infty)$
C) $[2, \infty)$
D) $[-2, \infty)$

Question 15

State the domain of the given function.

- $f(x)=\sqrt{-x-2}$

A) $[2, \infty)$
B) $[-2, \infty)$
C) $(-\infty,-2]$
D) $(-\infty, 2]$

Question 16

State the domain of the given function.

- $f(x)=9 x^{2}+9 x-9$

A) $(-\infty, \infty)$
B) all real numbers except 0
C) all whole numbers
D) $(0, \infty)$

Question 17

State the domain of the given function.

- $f(x)=\frac{4}{2 x-9}$

A) $(-\infty, \infty)$
B) all real numbers except $\frac{9}{2}$
C) $\left(\frac{9}{2}, \infty\right)$
D) all real numbers except $\frac{2}{9}$

Question 18

State the domain of the given function.

- $y=\frac{(x+3)(x-3)}{x^{2}+9}$

A) $(-\infty, \infty)$
B) $(-\infty, 3)$ or $(3, \infty)$
C) $(3, \infty)$
D) $(-\infty, 3)$

Question 19

Evaluate the function.

-Given that $f(x)=-8$ , find $f(3.1)$

A) -24.8
B) -8
C) 3.1
D) -4.9

Question 20

Evaluate the function.

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

A) -1
B) 3
C) 5
D) -3

Question 21

Evaluate the function.

-Find $f(-2)$ when $f(x)=2 x^{2}-2 x+6$

A) 6
B) 10
C) 18
D) 14

Question 22

Evaluate the function.

-Given that $f(x)=\sqrt{x+5}$ , find $f(-3)$

A) $\sqrt{2} \approx 4$
B) $\sqrt{5} \approx 2.2361$
C) $\sqrt{2} \approx 1$
D) $\sqrt{2} \approx 1.4142$

Question 23

Evaluate the function.

-Given that $f(x)=\sqrt{8-x}$ , find $f(1.4)$ .

A) $\sqrt{6.6} \approx 3.3$
B) $\sqrt{6.6} \approx 2.5690$
C) $\sqrt{8} \approx 2.8284$
D) $\sqrt{9.4} \approx 3.0659$

Question 24

Evaluate the function.

-Given that $f(x)=x^{3}-1.5 x^{2}+2.6 x-1$ , find $f(4)$ .

A) 49.4
B) 64.1
C) 76.6
D) 28.6

Question 25

Evaluate the function.

-Given that $f(x)=x^{4}-1.7 x^{2}-8.4 x$ , find $f(1.5)$ .

A) 21.4875
B) 13.8375
C) -9.0
D) -11.3625

Question 26

Evaluate the function.

-Given that $f(x)=\left|x^{3}-x^{2}-6 x-1\right|$ , find $f(-1.8)$

A) -0.728
B) 0.728
C) 3.968
D) 20.872

Question 27

Evaluate the function.

-Given that $f(x)=\frac{\sqrt{x^{2}+1}}{x-1}$ , find $f(3)$ .

A) $\frac{\sqrt{10}}{2} \approx 2.5$
B) $\frac{\sqrt{10}}{2} \approx 1.5811$
C) $\frac{\sqrt{10}}{2} \approx-1.5811$
D) $\frac{\sqrt{10}}{2} \approx 50.0000$

Question 28

Evaluate the function.

-Given that $f(x)=\sqrt{x}+\frac{3}{1-x}$ , find $f(3.8)$ .

A) $\sqrt{3.8}-\frac{15}{14} \approx 0.8286$
B) $\sqrt{3.8}-\frac{15}{14} \approx 13.3686$
C) $\sqrt{3.8}-\frac{15}{14} \approx 3.0208$
D) $\sqrt{3.8}-\frac{15}{14} \approx 0.8779$

Question 29

Use a graphing calculator to construct a table of values for the given function.

-Use a graphing calculator to display a table showing the (approximate) values of the function $f(x)=x^{3}-5 x^{2}-5 x$ at $4.3,4.7,5.1,5.5,5.9,6.3$ .

A)
B) C) D)

Question 30

Use a graphing calculator to construct a table of values for the given function.

-Use a graphing calculator to display a table showing the (approximate) values of the function $f(x)=\sqrt{x^{2}+4 x-2}$ at 2.1, 2.5, 2.9, 3.3, 3.7, 4.1.

A)
B) C) D)

Question 31

Evaluate the function.

-Given that $f(x)=\sqrt{5 x-6}$ , and $f(p)$ .

A) $\sqrt{5 p-6}$
B) $\sqrt{5 x-p}$
C) $\sqrt{\mathrm{px}-6}$
D) $5 p-6$

Question 32

Evaluate the function.

-Given that $f(x)=\frac{7}{6-x}$ , find $f(m)$ .

A) $\frac{7}{m-x}$
B) $\frac{m}{6-x}$
C) $\frac{7}{6-m}$
D) $\frac{m}{6-m}$

Question 33

Evaluate the function.

-Find $f(k)$ when: $f(x)=3 x^{2}+4 x+5$

A) $f(k)=3 k^{2}+4 k+25$
B) $f(k)=3 k^{2}+4 k+5$
C) $f(k)=9 k^{2}+16 k+25$
D) $f(k)=3 k^{2}+16 k+5$

Question 34

Evaluate the function.

-Given that $f(x)=3-8 x$ , find $f(-r)$ .

A) $3+8 r$
B) $r-8 x$
C) $3-8 r$
D) $3+\mathrm{rx}$

Question 35

Evaluate the function.

-given that $f(x)=\sqrt{-3 x}$ , find $f(-k)$ .

A) $\sqrt{-3 \mathrm{k}}$
B) $\sqrt{\mathrm{kx}}$
C) $\sqrt{3 \mathrm{k}}$
D) $\sqrt{-k x}$

Question 36

Evaluate the function.

-Given that $f(x)=3-8 x^{3}$ , find $f(-n)$ .

A) $3+8 n^{3}$
B) $3+n x^{3}$
C) $-n-8 x^{3}$
D) $3-8 n^{3}$

Question 37

Evaluate the function.

-Determine $g(a-1)$ when $g(x)=2 x-3$ .

A) $2 a-5$
B) $2 a+1$
C) $\frac{1}{2} a-3$
D) $2 a-3$

Question 38

Evaluate the function.

-Find $f(k-1)$ when: $f(x)=3 x^{2}+3 x+3$

A) $f(k-1)=-3 k^{2}+3 k+3$
B) $f(k-1)=3 k^{2}+12 k+9$
C) $f(k-1)=3 k^{2}-3 k+9$
D) $f(k-1)=3 k^{2}-3 k+3$

Question 39

Evaluate the function.

-Given that $f(x)=\sqrt{8-x}$ , find $f(m+2)$ .

A) $\sqrt{m+2}$
B) $\sqrt{6-m}$
C) $\sqrt{m+2-x}$
D) $\sqrt{10-m}$

Question 40

Evaluate the function.

-Given that $f(x)=\frac{1}{4-3 x}$ , find $f(r-3)$ .

A) $\frac{1}{r-3-3 x}$
B) $\frac{1}{1-3 r}$
C) $\frac{1}{13+3 b}$
D) $\frac{1}{13-3 r}$

Question 41

For the given function, find $\frac{f(x+h)-f(x)}{h}$ .

- $9 x-3$

A) 1
B) $\frac{h-6}{h}$
C) $\frac{9 h-6}{h}$
D) 9

Question 42

For the given function, find $\frac{f(x+h)-f(x)}{h}$ .

- $2-9 x$

A) $\frac{h-18 x}{h}$
B) 1
C) -9
D) $\frac{-9 h-18 x}{h}$

Question 43

For the given function, find $\frac{f(x+h)-f(x)}{h}$ .

- $x^{2}+2$

A) $2 x+h$
B) $\frac{h+4}{h}$
C) $2 x+h+4$
D) 1

Question 44

For the given function, find $\frac{f(x+h)-f(x)}{h}$ .

- $x^{2}-4 x$

A) $2 x-4+h$
B) $2 x+4+h$
C) $2 x+h$
D) $\frac{2 x h+h^{2}-4 h-8 x}{h}$

Question 45

For the given function, find $\frac{f(x+h)-f(x)}{h}$ .

- $3 x^{2}+3$

A) $6 x+3 h$
B) $3 \mathrm{~h}$
C) $\frac{6 x h+3 h^{2}+6}{h}$
D) 1

Question 46

Solve the problem.

-Suppose the cost of producing $x$ computers is $c(x)=2000+90 x-0.1 x^{2}$ . Find the cost of producing 80 computers.

A) $\$ 9136$
B) $\$ 1450$
C) $\$ 8560$
D) $\$ 9200$

Question 47

Solve the problem.

-If a rock is thrown vertically upward from the surface of the moon at a speed of $21 \mathrm{~m} / \mathrm{s}$ , its height after $t$ seconds will be $s(t)=21 t-0.8 t^{2}$ meters. Find its height after 6 seconds.

A) 90.0 meters
B) 125.2 meters
C) 102.96 meters
D) 97.2 meters

Question 48

Solve the problem.

-The water is drained from a tank by opening a valve at the bottom of the tank. The depth of the water in the tank thours after the valve is opened is $d(t)=6\left(1-\frac{t}{12}\right)^{2}$ meters. If the valve is opened at $1 \mathrm{pm}$ , what is the depth of water at $10 \mathrm{pm}$ ?

A) 2.62 meters
B) 1.50 meters
C) 0.38 meters
D) 0.17 meters

Question 49

Solve the problem.

-the size (in thousands) of a certain population in year $x$ is approximated by the function $h(x)=0.4 x^{2}+1.9 x+40$ (where $x=0$ corresponds to the year 1990). predict the size of the population in the year 1997 .

A) About 73
B) About 61,140
C) About 72,900
D) About 1,599,038

Question 50

Solve the problem.

-A cereal factory has weekly fixed costs of $\$ 33,000$ . It costs $\$ 1.28$ to produce each box of cereal. A box of cereal sells for $\$ 4.07$ . Find the rule of the cost function $\mathrm{c}(\mathrm{x})$ that gives the total weekly cost of producing $x$ boxes of cereal.

A) $c(x)=33,000+4.07 x$
B) $c(x)=33,000+1.28 x$
C) $c(x)=1.28 x$
D) $c(x)=33,000+2.79 x$

Question 51

Solve the problem.

-A cereal factory has weekly fixed costs of $\$ 22,000$ . It costs $\$ 1.26$ to produce each box of cereal. A box of cereal sells for $\$ 3.87$ . Find the rule of the revenue function $r(x)$ that gives the total weekly revenue from selling $x$ boxes of cereal.

A) $c(x)=22,000+2.61 x$
B) $c(x)=3.87 x$
C) $c(x)=2.61 x$
D) $c(x)=22,000+3.87 x$

Question 52

Solve the problem.

-A cereal factory has weekly fixed costs of $\$ 43,000$ . It costs $\$ 1.38$ to produce each box of cereal. A box of cereal sells for $\$ 3.94$ . Find the rule of the profit function $p(x)$ that gives the total weekly profit from $x$ boxes of cereal.

A) $p(x)=2.56 x-43,000$
B) $p(x)=2.56+43,000 x$
C) $p(x)=3.94 x-43,000$
D) $p(x)=2.56 x$

Question 53

Solve the problem.

-On a business trip, Jon must drive from his office to a clients's office, a distance of 204 miles. He sets off a $8 \mathrm{a} . \mathrm{m}$ . Suppose that he drives at a constant speed of $67 \mathrm{mph}$ . Find the rule of the function $f(t)$ that gives his distance from the client's office at time $t$ hours (with $t=0$ corresponding to 8 a.m.)

A) $f(t)=204-\frac{67}{t}$
B) $f(t)=204+67 t$
C) $f(t)=204-67 t$
D) $f(t)=67 t$

Question 54

Solve the problem.

-Janice is running a 8354 meter race. Assume that she runs at a constant speed of 309 meters per minute. Find the rule of the function $f(t)$ that gives her distance from the finishing line $t$ minutes after the start of the race.

A) $f(t)=8354+309 t$
B) $f(t)=309 t$
C) $f(t)=8354-\frac{309}{t}$
D) $f(t)=8354-309 t$

Question 55

Graph the linear function.

- $f(x)=-4 x+1$

A)
B)

Question 56

Graph the linear function.

- $g(x)=x-4$

A)
B)

Question 57

Graph the linear function.

- $h(x)=6 x$

A)
B)

Question 58

Graph the linear function.

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

A)
B)

Question 59

Graph the linear function.

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

A)
B)

Question 60

Graph the piecewise linear function.

- $f(x)= \begin{cases}-4, & x \geq 1 \\ x+2, & x<1\end{cases}$

A)
B)
C)
D)

Question 61

Graph the piecewise linear function.

- $f(x)=\left\{\begin{array}{lr}-2, & x \geq 1 \\ -x+4, & x<1\end{array}\right.$

A)
B)
C)
D)

Question 62

Graph the piecewise linear function.

- $f(x)= \begin{cases}5, & x \geq 1 \\ -1-x, & x<1\end{cases}$

A)
B)
C)
D)

Question 63

Graph the piecewise linear function.

- $f(x)= \begin{cases}x-4, & x>0 \\ 5, & x \leq 0\end{cases}$

A)
B)
C)
D)

Question 64

Graph the piecewise linear function.

- $f(x)= \begin{cases}1, & x \geq-1 \\ x-3, & x<-1\end{cases}$

A)
B)
C)
D)

Question 65

Graph the piecewise linear function.

- $f(x)= \begin{cases}x-1, & x>2 \\ -4, & x<2\end{cases}$

A)
B)
C)
D)

Question 66

Graph the piecewise linear function.

- $f(x)= \begin{cases}-1-x, & x \leq 2 \\ 1-2 x, & x>2\end{cases}$

A)
B)
C)
D)

Question 67

Graph the function.

- $f(x)=|x+5|$

A)
B)
C)
D)

Question 68

Graph the function.

- $f(x)=|x|-1$

A)
B)
C)
D)

Question 69

Graph the function.

- $f(x)=-|2 x|$

A)
B)
C)
D)

Question 70

Graph the function.

- $f(x)=|3 x-5|$

A)
B)
C)
D)

Question 71

Graph the function.

- $f(x)= \begin{cases}2 x & \text { if } x \leq-1 \\ -|x| & \text { if } x>-1\end{cases}$

A)
B)
C)
D)

Question 72

Graph the function.

- $f(x)= \begin{cases}-2 x & \text { if } x<-2 \\ |x| & \text { if } x \geq-2\end{cases}$

A)
B)
C)
D)

Question 73

Graph the function.

- $y=|-4-x|$

A)
B)
C)
D)

Question 74

Graph the function.

- $y=3|x|-7$

A)
B)
C)
D)

Question 75

Graph the function.

- $y=|x-3|-8$

A)
B)
C)
D)

Question 76

Graph the function.

- $y=-|5-x|$

A)
B)
C)
D)

Question 77

Graph the function.

- $y=[x]+1$

A)
B)

Question 78

Graph the function.

- $y=[x+1]$

A)
B)

Question 79

Graph the function.

- $y=[x]-1$

A)
B)

Question 80

Graph the function.

- $y=[x-1]$

A)
B)