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College Algebra

James Stewart, Lothar Redlin, Saleem Watson

Chapter 2

Functions - all with Video Answers

Educators

AG

Section 1

Functions

03:26

Problem 1

If $f(x)=x^{3}+1,$ then.
a. the value of $f$ at $x=-1$ is $f(-\infty)=$ _____
b. the value of $f$ at $x=2$ is $f(-\infty)=$ _____
c. the net change in the value of $f$ between $x=-1$ and $x=2$ is $f$ ( ______ ) $-f$ ( ______ ) $=$ _______.

AG
Ankit Gupta
Numerade Educator
01:13

Problem 2

For a function $f,$ the set of all possible inputs is called the ______ of $f,$ and the set of all possible outputs is called the _______ of $f.$

Shrey Kalra
Shrey Kalra
Numerade Educator
02:00

Problem 3

a. Which of the following functions have 5 in their domain?
$$
f(x)=x^{2}-3 x \quad g(x)=\frac{x-5}{x} \quad h(x)=\sqrt{x-10}
$$
b. For the functions from part (a) that $d o$ have 5 in their domain, find the value of the function at 5.

James Kiss
James Kiss
Numerade Educator
04:55

Problem 4

A function is given algebraically by the formula $f(x)=(x-4)^{2}+3 .$ Complete these other ways to represent $f:$
a. Verbal: "Subtract 4, then ____ and ____.
b. Numerical:
$$\begin{array}{|c|c|}
\hline x & f(x) \\
\hline 0 & 19 \\
2 & \\
4 & \\
6 & \\
\hline
\end{array}$$

AG
Ankit Gupta
Numerade Educator
03:56

Problem 5

A function $f$ is a rule that assigns to each element $x$ in a set $A$ exactly $(i)$ element(s) called $f(x)$ in a set $B$. Which of the following tables defines $y$ as a function of $x ?$
$$\begin{array}{|c|c|}
\hline x & y \\
\hline 1 & 5 \\
2 & 7 \\
3 & 6 \\
4 & 8 \\
\hline
\end{array}$$
$$\begin{array}{|c|c|}
\hline x & y \\
\hline 1 & 5 \\
1 & 7 \\
2 & 6 \\
3 & 8 \\
\hline
\end{array}$$

AG
Ankit Gupta
Numerade Educator
00:56

Problem 6

Yes or No? If No, give a reason. Let $f$ be a function.
a. Is it possible that $f(1)=5$ and $f(2)=5 ?$
b. Is it possible that $f(1)=5$ and $f(1)=6 ?$

James Kiss
James Kiss
Numerade Educator
View

Problem 7

Express the rule in function notation. (For example, the rule "square, then subtract 5 " is expressed as the function $f(x)=x^{2}-5 .$ )
Multiply by 3, then subtract 5

Kathleen Carty
Kathleen Carty
Numerade Educator
01:55

Problem 8

Express the rule in function notation. (For example, the rule "square, then subtract 5 " is expressed as the function $f(x)=x^{2}-5 .$ )
Square, then add 2

AG
Ankit Gupta
Numerade Educator
02:24

Problem 9

Express the rule in function notation. (For example, the rule "square, then subtract 5 " is expressed as the function $f(x)=x^{2}-5 .$ )
Subtract 1, then square

AG
Ankit Gupta
Numerade Educator
02:26

Problem 10

Express the rule in function notation. (For example, the rule "square, then subtract 5 " is expressed as the function $f(x)=x^{2}-5 .$ )
Add 1, take the square root, then divide by 6

AG
Ankit Gupta
Numerade Educator
02:07

Problem 11

Express the function (or rule) in words.
$$f(x)=2 x+3$$

AG
Ankit Gupta
Numerade Educator
02:07

Problem 12

Express the function (or rule) in words.
$$g(x)=\frac{x+2}{3}$$

AG
Ankit Gupta
Numerade Educator
00:37

Problem 13

Express the function (or rule) in words.
$$h(x)=5(x+1)$$

Savannah Payne
Savannah Payne
Numerade Educator
02:24

Problem 14

Express the function (or rule) in words.
$$k(x)=\frac{x^{2}-4}{3}$$

AG
Ankit Gupta
Numerade Educator
View

Problem 15

Draw a machine diagram for the function.
$$f(x)=\sqrt{x-1}$$

JD
Josie Dalrymple
Numerade Educator
02:22

Problem 16

Draw a machine diagram for the function.
$$f(x)=\frac{3}{x-2}$$

Sanchit Jain
Sanchit Jain
Numerade Educator
03:39

Problem 17

Complete the table.
$$f(x)=2(x-1)^{2}$$
$$\begin{array}{|c|c|}
\hline x & f(x) \\
\hline-1 & \\
0 & \\
1 & \\
2 & \\
3 & \\
\hline
\end{array}$$

AG
Ankit Gupta
Numerade Educator
04:27

Problem 18

Complete the table.
$$g(x)=|2 x+3|$$
$$\begin{array}{|c|c|}
\hline x & g(x) \\
\hline-3 & \\
-2 & \\
0 & \\
1 & \\
3 & \\
\hline
\end{array}$$

AG
Ankit Gupta
Numerade Educator
02:59

Problem 19

Evaluate the function at the indicated values.
$$f(x)=x^{2}-6 ; \quad f(-3), f(3), f(0), f\left(\frac{1}{2}\right)$$

AG
Ankit Gupta
Numerade Educator
02:59

Problem 20

Evaluate the function at the indicated values.
$$f(x)=x^{3}+2 x ; \quad f(-2), f(-1), f(0), f\left(\frac{1}{2}\right)$$

AG
Ankit Gupta
Numerade Educator
03:50

Problem 21

Evaluate the function at the indicated values.
$$f(x)=\frac{1-2 x}{3} ; \quad f(2), f(-2), f\left(\frac{1}{2}\right), f(a), f(-a), f(a-1)$$

AG
Ankit Gupta
Numerade Educator
04:37

Problem 22

Evaluate the function at the indicated values.
$$h(x)=\frac{x^{2}+4}{5} ; \quad h(2), h(-2), h(a), h(-x), h(a-2), h(\sqrt{x})$$

AG
Ankit Gupta
Numerade Educator
03:23

Problem 23

Evaluate the function at the indicated values.
$$f(x)=x^{2}+2 x ; \quad f(0), f(3), f(-3), f(a), f(-x), f\left(\frac{1}{a}\right)$$

AG
Ankit Gupta
Numerade Educator
03:56

Problem 24

Evaluate the function at the indicated values.
$$-h(t)=t+\frac{1}{t} ; \quad h(-1), h(2), h\left(\frac{1}{2}\right), h(x-1), h\left(\frac{1}{x}\right)$$

AG
Ankit Gupta
Numerade Educator
04:52

Problem 25

Evaluate the function at the indicated values.
$$g(x)=\frac{1-x}{1+x} ; \quad g(2), g(-1), g\left(\frac{1}{2}\right), g(a), g(a-1), g\left(x^{2}-1\right)$$

AG
Ankit Gupta
Numerade Educator
04:03

Problem 26

Evaluate the function at the indicated values.
$$g(t)=\frac{t+2}{t-2} ; \quad g(-2), g(2), g(0), g(a), g\left(a^{2}-2\right), g(a+1)$$

AG
Ankit Gupta
Numerade Educator
05:32

Problem 27

Evaluate the function at the indicated values.
$$k(x)=-x^{2}-2 x+3 ; \quad k(0), \quad k(2), k(-2), k(\sqrt{2}), k(a+2), k(-x), k\left(x^{2}\right)$$

AG
Ankit Gupta
Numerade Educator
05:49

Problem 28

Evaluate the function at the indicated values.
$$k(x)=2 x^{3}-3 x^{2} ; \quad k(0), k(3), k(-3), k\left(\frac{1}{2}\right), k\left(\frac{a}{2}\right), k(-x), k\left(x^{3}\right)$$

AG
Ankit Gupta
Numerade Educator
04:08

Problem 29

Evaluate the function at the indicated values.
$$f(x)=2|x-1| ; \quad f(-2), f(0), f\left(\frac{1}{2}\right), f(2), f(x+1), f\left(x^{2}+2\right)$$

AG
Ankit Gupta
Numerade Educator
04:48

Problem 30

Evaluate the function at the indicated values.
$$f(x)=\frac{|x|}{x} ; \quad f(-2), f(-1), f(0), f(5), f\left(x^{2}\right), f\left(\frac{1}{x}\right)$$

AG
Ankit Gupta
Numerade Educator
03:37

Problem 31

Evaluate the piecewise defined function at the indicated values.
$$f(x)=\left\{\begin{array}{ll}
x^{2} & \text { if } x<0 \\
x+1 & \text { if } x \geq 0
\end{array}\right.$$
$$f(-2), f(-1), f(0), f(1), f(2)$$

AG
Ankit Gupta
Numerade Educator
02:37

Problem 32

Evaluate the function at the indicated values.
$$f(x)=\left\{\begin{array}{ll}
5 & \text { if } x \leq 2 \\
2 x-3 & \text { if } x>2
\end{array}\right.$$
$$f(-3), f(0), f(2), f(3), f(5)$$

AG
Ankit Gupta
Numerade Educator
03:44

Problem 33

Evaluate the function at the indicated values.
$$f(x)=\left\{\begin{array}{ll}
x^{2}+2 x & \text { if } x \leq-1 \\
x & \text { if }-1<x \leq 1 \\
-1 & \text { if } x>1
\end{array}\right.$$
$$f(-4), f\left(-\frac{3}{2}\right), f(-1), f(0), f(25)$$

AG
Ankit Gupta
Numerade Educator
02:53

Problem 34

Evaluate the function at the indicated values.
$$\begin{aligned}
&f(x)=\left\{\begin{array}{ll}
3 x & \text { if } x<0 \\
x+1 & \text { if } 0 \leq x \leq 2 \\
(x-2)^{2} & \text { if } x>2
\end{array}\right.\\
&f(-5), f(0), f(1), f(2), f(5)
\end{aligned}$$

AG
Ankit Gupta
Numerade Educator
02:09

Problem 35

Use the function to evaluate the indicated expressions inputs.
$$f(x)=x^{2}+1 ; \quad f(x+2), f(x)+f(2)$$

AG
Ankit Gupta
Numerade Educator
01:06

Problem 36

Use the function to evaluate the indicated expressions inputs.
$$f(x)=3 x-1 ; \quad f(2 x), 2 f(x)$$

AG
Ankit Gupta
Numerade Educator
01:29

Problem 37

Use the function to evaluate the indicated expressions inputs.
$$f(x)=x+4 ; \quad f\left(x^{2}\right),(f(x))^{2}$$

AG
Ankit Gupta
Numerade Educator
01:05

Problem 38

Use the function to evaluate the indicated expressions inputs.
$$f(x)=6 x-18 ; \quad f\left(\frac{x}{3}\right), \frac{f(x)}{3}$$

AG
Ankit Gupta
Numerade Educator
02:02

Problem 39

Find the net change in the value of the function between the given inputs.
$f(x)=3 x-2 ;$ from 1 to 5

William Semus
William Semus
Numerade Educator
01:31

Problem 40

Find the net change in the value of the function between the given inputs.
$f(x)=4-5 x ;$ from 3 to 5

James Kiss
James Kiss
Numerade Educator
01:16

Problem 41

Find the net change in the value of the function between the given inputs.
$g(t)=1-t^{2} ;$ from -2 to 5

James Kiss
James Kiss
Numerade Educator
01:39

Problem 42

Find the net change in the value of the function between the given inputs.
$h(t)=t^{2}+5 ;$ from -3 to 6

James Kiss
James Kiss
Numerade Educator
02:19

Problem 43

Find $f(a), f(a+h),$ and the difference quotient $\frac{f(a+h)-f(a)}{h},$ where $h \neq 0.$
$$f(x)=5-2 x$$

Willis James
Willis James
Numerade Educator
02:25

Problem 44

Find $f(a), f(a+h),$ and the difference quotient $\frac{f(a+h)-f(a)}{h},$ where $h \neq 0.$
$$f(x)=3 x^{2}+2$$

James Kiss
James Kiss
Numerade Educator
01:15

Problem 45

Find $f(a), f(a+h),$ and the difference quotient $\frac{f(a+h)-f(a)}{h},$ where $h \neq 0.$
$$f(x)=5$$

James Kiss
James Kiss
Numerade Educator
02:48

Problem 46

Find $f(a), f(a+h),$ and the difference quotient $\frac{f(a+h)-f(a)}{h},$ where $h \neq 0.$
$$f(x)=\frac{1}{x+1}$$

James Kiss
James Kiss
Numerade Educator
02:39

Problem 47

Find $f(a), f(a+h),$ and the difference quotient $\frac{f(a+h)-f(a)}{h},$ where $h \neq 0.$
$$f(x)=\frac{x}{x+1}$$

James Kiss
James Kiss
Numerade Educator
05:18

Problem 48

Find $f(a), f(a+h),$ and the difference quotient $\frac{f(a+h)-f(a)}{h},$ where $h \neq 0.$
$$f(x)=\frac{2 x}{x-1}$$

Anas Venkitta
Anas Venkitta
Numerade Educator
03:38

Problem 49

Find $f(a), f(a+h),$ and the difference quotient $\frac{f(a+h)-f(a)}{h},$ where $h \neq 0.$
$$f(x)=3-5 x+4 x^{2}$$

James Kiss
James Kiss
Numerade Educator
02:58

Problem 50

Find $f(a), f(a+h),$ and the difference quotient $\frac{f(a+h)-f(a)}{h},$ where $h \neq 0.$
$$f(x)=x^{3}$$

James Kiss
James Kiss
Numerade Educator
01:06

Problem 51

Find the domain and range of the function.
$$f(x)=3 x$$

Carson Merrill
Carson Merrill
Numerade Educator
01:29

Problem 52

Find the domain and range of the function.
$$f(x)=5 x^{2}+4$$

James Kiss
James Kiss
Numerade Educator
01:02

Problem 53

Find the domain and range of the function.
$$f(x)=3 x, \quad-2 \leq x \leq 6$$

James Kiss
James Kiss
Numerade Educator
01:48

Problem 54

Find the domain and range of the function.
$$f(x)=5 x^{2}+4, \quad 0 \leq x \leq 2$$

James Kiss
James Kiss
Numerade Educator
00:59

Problem 55

Find the domain of the function.
$$f(x)=\frac{1}{x-3}$$

James Kiss
James Kiss
Numerade Educator
01:19

Problem 56

Find the domain of the function.
$$f(x)=\frac{1}{3 x-6}$$

James Kiss
James Kiss
Numerade Educator
02:19

Problem 57

Find the domain of the function.
$$f(x)=\frac{x+2}{x^{2}-1}$$

James Kiss
James Kiss
Numerade Educator
02:16

Problem 58

Find the domain of the function.
$$f(x)=\frac{x^{4}}{x^{2}+x-6}$$

James Kiss
James Kiss
Numerade Educator
01:07

Problem 59

Find the domain of the function.
$$f(t)=\sqrt{t+1}$$

James Kiss
James Kiss
Numerade Educator
01:20

Problem 60

Find the domain of the function.
$$g(t)=\sqrt{t^{2}+9}$$

James Kiss
James Kiss
Numerade Educator
00:52

Problem 61

Find the domain of the function.
$$f(t)=\sqrt[3]{t-1}$$

James Kiss
James Kiss
Numerade Educator
01:09

Problem 62

Find the domain of the function.
$$g(x)=\sqrt{7-3 x}$$

James Kiss
James Kiss
Numerade Educator
01:21

Problem 63

Find the domain of the function.
$$f(x)=\sqrt{1-2 x}$$

James Kiss
James Kiss
Numerade Educator
01:48

Problem 64

Find the domain of the function.
$$g(x)=\sqrt{x^{2}-4}$$

James Kiss
James Kiss
Numerade Educator
01:25

Problem 65

Find the domain of the function.
$$g(x)=\frac{\sqrt{x}}{2 x^{2}+x-1}$$

AG
Ankit Gupta
Numerade Educator
02:29

Problem 66

Find the domain of the function.
$$g(x)=\frac{\sqrt{x}}{2 x^{2}+x-1}$$

AG
Ankit Gupta
Numerade Educator
04:35

Problem 67

Find the domain of the function.
$$g(x)=\sqrt[4]{x^{2}-6 x}$$

James Kiss
James Kiss
Numerade Educator
05:12

Problem 68

Find the domain of the function.
$$g(x)=\sqrt{x^{2}-2 x-8}$$

Derek Follett
Derek Follett
Numerade Educator
01:40

Problem 69

Find the domain of the function.
$$f(x)=\frac{3}{\sqrt{x-4}}$$

James Kiss
James Kiss
Numerade Educator
01:50

Problem 70

Find the domain of the function.
$$f(x)=\frac{x^{2}}{\sqrt{6-x}}$$

James Kiss
James Kiss
Numerade Educator
01:43

Problem 71

Find the domain of the function.
$$f(x)=\frac{(x+1)^{2}}{\sqrt{2 x-1}}$$

James Kiss
James Kiss
Numerade Educator
02:40

Problem 72

Find the domain of the function.
$$f(x)=\frac{x}{\sqrt[4]{9-x^{2}}}$$

AG
Ankit Gupta
Numerade Educator
02:06

Problem 73

A verbal description of a function is given. Find
a. algebraic,
b. numerical, and
c. graphical representations for the function.
To evaluate $f(x)$, divide the input by 3 and add $\frac{2}{3}$ to the result.

AG
Ankit Gupta
Numerade Educator
02:27

Problem 74

A verbal description of a function is given. Find
a. algebraic,
b. numerical, and
c. graphical representations for the function.
To evaluate $g(x)$, subtract 4 from the input and multiply the result by $\frac{3}{4}$.

AG
Ankit Gupta
Numerade Educator
02:21

Problem 75

A verbal description of a function is given. Find
a. algebraic,
b. numerical, and
c. graphical representations for the function.
Let $T(x)$ be the amount of sales tax charged in Lemon County on a purchase of $x$ dollars. To find the tax, take $8 \%$ of the purchase price.

AG
Ankit Gupta
Numerade Educator
02:26

Problem 76

A verbal description of a function is given. Find
a. algebraic,
b. numerical, and
c. graphical representations for the function.
Let $V(d)$ be the volume of a sphere of diameter $d .$ To find the volume, take the cube of the diameter, then multiply by $\pi$ and divide by 6.

AG
Ankit Gupta
Numerade Educator
01:13

Problem 77

Find the domain and range of $f.$
$$f(x)=\left\{\begin{array}{ll}
1 & \text { if } x \text { is rational } \\
5 & \text { if } x \text { is irrational }
\end{array}\right.$$

James Kiss
James Kiss
Numerade Educator
01:25

Problem 78

Find the domain and range of $f.$
$$f(x)=\left\{\begin{array}{l}
1 \text { is } x \text { is antonain } \\
5 x \text { is ismanold }
\end{array}\right.$$

Brad Bailey
Brad Bailey
Numerade Educator
04:18

Problem 79

A tank holds 50 gal of water, which drains from a leak at the bottom, causing the tank to empty in 20 min. The tank drains faster when it is nearly full because the pressure on the leak is greater. Torricelli's Law gives the volume of water remaining in the tank after $t$ minutes as
$$
V(t)=50\left(1-\frac{t}{20}\right)^{2} \quad 0 \leq t \leq 20
$$
a. Find $V(0)$ and $V(20)$
b. What do your answers to part (a) represent?
c. Make a table of values of $V(t)$ for $t=0,5,10,15,20$
d. Find the net change in the volume $V$ as $t$ changes from 0 min to 20 min.

AG
Ankit Gupta
Numerade Educator
01:06

Problem 80

The surface area $S$ of a sphere is a function of its radius $r$ given by
$$
S(r)=4 \pi r^{2}
$$
a. Find $S(2)$ and $S(3)$
b. What do your answers in part (a) represent?

James Kiss
James Kiss
Numerade Educator
02:37

Problem 81

Relativity According to the Theory of Relativity, the length $L$ of an object is a function of its velocity $v$ with respect to an observer. For an object whose length at rest is $10 \mathrm{m}$, the function is given by
$$
L(v)=10 \sqrt{1-\frac{v^{2}}{c^{2}}}
$$
where $c$ is the speed of light $(300,000 \mathrm{km} / \mathrm{s}).$
a. Find $L(0.5 c), L(0.75 c),$ and $L(0.9 c)$
b. How does the length of an object change as its velocity increases?

AG
Ankit Gupta
Numerade Educator
04:01

Problem 82

Pupil Size When the brightness $x$ of a light source is increased, the eye reacts by decreasing the Tadius $R$ of the pupil. The dependence of $R$ on $x$ is given by the function
$$
R(x)=\sqrt{\frac{13+7 x^{0.4}}{1+4 x^{0.4}}}
$$
where $R$ is measured in millimeters and $x$ is measured in appropriate units of brightness.
a. Find $R(1), R(10),$ and $R(100)$
b. Make a table of values of $R(x)$
c. Find the net change in the radius $R$ as $x$ changes from 10 to 100 .

AG
Ankit Gupta
Numerade Educator
04:18

Problem 83

Blood Flow As blood moves through a vein or an artery, its velocity $v$ is greatest along the central axis and decreases as the distance $r$ from the central axis increases (see the figure). The formula that gives $v$ as a function of $r$ is called the law of laminar flow. For an artery with radius $0.5 \mathrm{cm},$ the relationship between $v(\mathrm{in} \mathrm{cm} / \mathrm{s})$ and $r(\mathrm{in} \mathrm{cm})$ is given by the function
$$
v(r)=18,500\left(0.25-r^{2}\right) \quad 0 \leq r \leq 0.5
$$
a. Find $v(0.1)$ and $v(0.4)$
b. What do your answers to part.(a) tell you about the flow of blood in this artery?
c. Make a table of values of $v(r)$ for $r=0,0.1,0.2,0.3,0.4,0.5$
d. Find the net change in the velocity $v$ as $r$ changes from $0.1 \mathrm{cm}$ to $0.5 \mathrm{cm}.$

AG
Ankit Gupta
Numerade Educator
02:51

Problem 84

How Far Can You See? Because of the curvature of the earth, the maximum distance $D$ that you can see from the top of a tall building or from an airplane at height $h$ is given by the function
$$
D(h)=\sqrt{2 r h+h^{2}}
$$
where $r=3960 \mathrm{mi}$ is the radius of the earth and $D$ and $h$ are measured in miles.
a. Find $D(0.1)$ and $D(0.2)$
b. How far can you see from the observation deck of Toronto's CN Tower, 1135 ft above the ground?
c. Commercial aircraft fly at an altitude of about 7 mi. How far can the pilot see?
d. Find the net change in the value of distance $D$ as $h$ changes from $1135 \mathrm{ft}$ to $7 \mathrm{mi}$.

James Kiss
James Kiss
Numerade Educator
02:51

Problem 85

In a certain country, income tax $T$ is assessed according to the following function of income $x$ :
$T(x)=\left\{\begin{array}{ll}0 & \text { if } 0 \leq x \leq 10,000 \\ 0.08 x & \text { if } 10,000<x \leq 20,000 \\ 1600+0.15 x & \text { if } 20,000<x\end{array}\right.$
a. Find $T(5,000), T(12,000),$ and $T(25,000)$
b. What do your answers in part (a) represent?

AG
Ankit Gupta
Numerade Educator
02:48

Problem 86

Internet Purchases An Internet bookstore charges $\$ 15$ shipping for orders under $\$ 100$ but provides free shipping for orders of $\$ 100$ or more. The cost $C$ of an order is a function of the total price $x$ of the books purchased, given by
$$
C(x)=\left\{\begin{array}{ll}
x+15 & \text { if } x<100 \\
x & \text { if } x \geq 100
\end{array}\right.
$$
a. Find $C(75), C(90), C(100),$ and $C(105)$
b. What do your answers in part (a) represent?

AG
Ankit Gupta
Numerade Educator
02:03

Problem 87

cost of a Hotel Stay A hotel chain charges $\$ 75$ each night for the first two nights and $\$ 50$ for each additional night's stay. The total cost $T$ is a function of the number of nights $x$ that a guest stays.
a. Complete the expressions in the following piecewise defined function.
$$
T(x)=\left\{\begin{array}{ll}
& \text { if } 0 \leq x \leq 2 \\
& \text { if } x>2
\end{array}\right.
$$
b. Find $T(2), T(3),$ and $T(5)$
c. What do your answers in part (b) represent?

James Kiss
James Kiss
Numerade Educator
03:14

Problem 88

Speeding Tickets In a certain state the maximum speed permitted on freeways is $65 \mathrm{mi} / \mathrm{h}$, and the minimum is $40 \mathrm{mi} / \mathrm{h}$. The fine $F$ for violating these limits is $\$ 15$ for every mile above the maximum or below the minimum.
a. Complete the expressions in the following piece wise defined function, where $x$ is the speed at which you are driving.
b. Find $F(30), F(50),$ and $F(75)$
c. What do your answers in part (b) represent?

AG
Ankit Gupta
Numerade Educator
01:28

Problem 89

A home owner mows the lawn every Wednesday afternoon. Sketch a rough graph of the height of the grass as a function of time over the course of a four-week period beginning on a Sunday.

James Kiss
James Kiss
Numerade Educator
02:36

Problem 90

Temperature Change Then you take the pie out and let it cool before eating it. Sketch a rough graph of the temperature of the pie as a function of time.

AG
Ankit Gupta
Numerade Educator
01:29

Problem 91

Temperature readings $T$ (in $^{\circ} \mathrm{F}$ ) were recorded every 2 hours from midnight to noon in Atlanta, Georgia, on March $18,2014 .$ The time $t$ was measured in hours from midnight. Sketch a rough graph of $T$ as a function of $t.$
$$\begin{array}{|c|c|c|c|c|c|c|c|}
\hline t & 0 & 2 & 4 & 6 & 8 & 10 & 12 \\
\hline T & 58 & 57 & 53 & 50 & 51 & 57 & 61 \\
\hline
\end{array}$$

AG
Ankit Gupta
Numerade Educator
01:37

Problem 92

The population $P$ (in thousands) of San Jose, California, from 1980 to 2010 is shown in the table. (Midyear estimates are given.) Draw a rough graph of $P$ as a function of time $t.$
$$\begin{array}{|c|c|c|c|c|c|c|c|}
\hline t & 1980 & 1985 & 1990 & 1995 & 2000 & 2005 & 2010 \\
\hline P & 629 & 714 & 782 & 825 & 895 & 901 & 946 \\
\hline
\end{array}$$

AG
Ankit Gupta
Numerade Educator
01:44

Problem 93

At the beginning of this section we discussed three examples of everyday, ordinary functions: Height is a function of age, temperature is a function of date, and postage cost is a function of weight. Give three other examples of functions from everyday life.

AG
Ankit Gupta
Numerade Educator
03:44

Problem 94

In the box Four Ways to Represented Function we represented four different functions verbally, algebraically, visually, and numerically. Think of a function that can be represented in all four ways, and give the four representations.

AG
Ankit Gupta
Numerade Educator
02:24

Problem 95

Discuss: Piece wise Defined Functions we worked with real-world situations modeled by piece wise defined functions. Find other examples of real-world situations that can be modeled by piece wise defined functions, and express the models in function notation.

AG
Ankit Gupta
Numerade Educator