match the set with the most appropriate choice from the column on the right.

$$

\{x | x<-2 \text { or } x>2\}

$$

Darian K.

Numerade Educator

match the set with the most appropriate choice from the column on the right.

$$

\{x | x<-2 \text { and } x>2\}

$$

Darian K.

Numerade Educator

match the set with the most appropriate choice from the column on the right.

$$

\{x | x>-2\} \cap\{x | x<2\}

$$

Darian K.

Numerade Educator

match the set with the most appropriate choice from the column on the right.

$$

\{x | x \leq-2\} \cup\{x | x \geq 2\}

$$

Darian K.

Numerade Educator

match the set with the most appropriate choice from the column on the right.

$$

\{x | x \leq-2\} \cup\{x | x \leq 2\}

$$

Darian K.

Numerade Educator

match the set with the most appropriate choice from the column on the right.

$$

\{x | x \leq-2\} \cap\{x | x \leq 2\}

$$

Darian K.

Numerade Educator

match the set with the most appropriate choice from the column on the right.

$$

\{x | x \geq-2\} \cap\{x | x \geq 2\}

$$

Darian K.

Numerade Educator

match the set with the most appropriate choice from the column on the right.

$$

\{x | x \geq-2\} \cup\{x | x \geq 2\}

$$

Darian K.

Numerade Educator

match the set with the most appropriate choice from the column on the right.

$$

\{x | x \leq 2\} \text { and }\{x | x \geq-2\}

$$

Darian K.

Numerade Educator

match the set with the most appropriate choice from the column on the right.

$$

\{x | x \leq 2\} \text { or }\{x | x \geq-2\}

$$

Darian K.

Numerade Educator

Solve each inequality using the given graph.

$$

f(x) \geq g(x)

$$

Darian K.

Numerade Educator

Solve each inequality using the given graph.

$$

y_{1} \geq y_{2}

$$

Darian K.

Numerade Educator

The graphs of $f(x)=2 x+1, g(x)=-\frac{1}{2} x+3$

and $h(x)=x-1$ are as shown below. Solve each inequality, referring only to the figure.

a) $2 x+1 \leq x-1$

b) $x-1>-\frac{1}{2} x+3$

c) $-\frac{1}{2} x+3<2 x+1$

Darian K.

Numerade Educator

The graphs of $y_{1}=-\frac{1}{2} x+5, y_{2}=x-1,$ and $y_{3}=2 x-3$ are as shown below. Solve each inequality, referring only to the figure.

a) $-\frac{1}{2} x+5>x-1$

b) $x-1 \leq 2 x-3$

c) $2 x-3 \geq-\frac{1}{2} x+5$

Darian K.

Numerade Educator

Use a graph to estimate the solution in each of the following. Be sure to use graph paper and a straightedge if graphing by hand.

Show Business. A band receives $\$ 750$ plus $15 \%$ of receipts over $\$ 750$ for playing a club date. If a club charges a $\$ 6$ cover charge, how many people must attend in order for the band to receive at least $\$ 1200 ?$

Darian K.

Numerade Educator

Use a graph to estimate the solution in each of the following. Be sure to use graph paper and a straightedge if graphing by hand.

Temperature Conversion. The function

$C(F)=\frac{5}{9}(F-32)$

can be used to find the Celsius temperature $C(F)$ that corresponds to $F^{\circ}$ Fahrenheit.

a) Gold is solid at Celsius temperatures less than $1063^{\circ} \mathrm{C} .$ Find the Fahrenheit temperatures for which gold is solid.

b) Silver is solid at Celsius temperatures less than $960.8^{\circ} \mathrm{C} .$ Find the Fahrenheit temperatures for which silver is solid.

Darian K.

Numerade Educator

Use a graph to estimate the solution in each of the following. Be sure to use graph paper and a straightedge if graphing by hand.

A musement Park Attendance. The table below lists the estimated annual ridership at amusement parks for various years. Use linear regression to find a linear function that can be used to predict the ridership $r(x),$ in billions, where $x$ is the number of years after $2000 .$ Then predict those years in which there will be fewer than 1.5 billion riders.

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Use a graph to estimate the solution in each of the following. Be sure to use graph paper and a straightedge if graphing by hand.

Smoking. The table below lists the percent of teenagers in the United States who smoked cigarettes during various years. Use linear regression to find a linear function that can be used to predict the percent $p(x)$ of teenagers who smoked, where $x$ is the number of years after 2000 . Then predict those years in which the Healthy People 2010 goal of no more than $16 \%$ teenage smokers will be met.

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Use a graph to estimate the solution in each of the following. Be sure to use graph paper and a straightedge if graphing by hand.

Advertising. The table below lists advertising revenue for newspapers and the Internet for various years. Use linear regression to find two linear functions that can be used to estimate advertising revenue $n(x),$ in billions of dollars, for newspapers and $t(x)$ for the Internet, where $x$ is the number of years after 2006 . Then predict the years for which advertising revenue for the Internet will exceed that for newspapers.

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Use a graph to estimate the solution in each of the following. Be sure to use graph paper and a straightedge if graphing by hand.

Income. The table below lists the median adjusted household income for unmarried and married men for various years. Use linear regression to find two linear functions that can be used to estimate the median household earnings $u(x)$ for unmarried men and $m(x)$ for married men, where $x$ is the number of years after $1970 .$ Then estimate the years for which the household earnings for married men exceeds that for unmarried men.

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Use a graph to estimate the solution in each of the following. Be sure to use graph paper and a straightedge if graphing by hand.

100-Meter Freestyle. The table below lists the world record for the women's 100 -meter freestyle long-course swim for various years. Use linear regression to find a linear function that can be used to predict the world record $x$ years after $1990 .$ Then predict those years in which the world record will be less than 50 sec.

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Use a graph to estimate the solution in each of the following. Be sure to use graph paper and a straightedge if graphing by hand.

Mile Run. The table below lists the world record for the mile run for various years. Use linear regression to find a linear function that can be used to predict the world record for the mile run $x$ years after $1954 .$ Then predict those years in which the world record will be less than $3.5 \mathrm{min}$.

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Find each indicated intersection or union.

$$

\{0,5,10,15\} \cup\{5,15,20\}

$$

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Find each indicated intersection or union.

$$

\{2,5,9,13\} \cap\{5,8,10\}

$$

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Find each indicated intersection or union.

$$

\{a, b, c, d, e, f\} \cap\{b, d, f\}

$$

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Find each indicated intersection or union.

$$

\{r, s, t\} \cup\{r, u, t, s, v\}

$$

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Find each indicated intersection or union.

$$

\{m, n, o, p\} \cap\{m, o, p\}

$$

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Find each indicated intersection or union.

$$

\{3,6,9,12\} \cap\{5,10,15\}

$$

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Find each indicated intersection or union.

$$

\{3,5,7\} \cup \varnothing

$$

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Find each indicated intersection or union.

$$

\{3,5,7\} \cap \varnothing

$$

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Graph and write interval notation for each compound inequality.

$$

3<x<7

$$

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Graph and write interval notation for each compound inequality.

$$

0 \leq y \leq 4

$$

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Graph and write interval notation for each compound inequality.

$$

-6 \leq y \leq 0

$$

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Graph and write interval notation for each compound inequality.

$$

-9 \leq x<-5

$$

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Graph and write interval notation for each compound inequality.

$$

x<-1 \text { or } x>4

$$

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Graph and write interval notation for each compound inequality.

$$

x<-5 \text { or } x>1

$$

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Graph and write interval notation for each compound inequality.

$$

x \leq-2 \text { or } x>1

$$

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Graph and write interval notation for each compound inequality.

$$

x \leq-5 \text { or } x>2

$$

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Graph and write interval notation for each compound inequality.

$$

x>-2 \text { and } x<4

$$

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Graph and write interval notation for each compound inequality.

$$

x>-7 \text { and } x<-2

$$

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Graph and write interval notation for each compound inequality.

$$

-4 \leq-x<2

$$

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Graph and write interval notation for each compound inequality.

$$

3>-x \geq-1

$$

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Graph and write interval notation for each compound inequality.

$$ 5> a or a>7 $$

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Graph and write interval notation for each compound inequality.

$$

t \geq 2 \text { or }-3>t

$$

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Graph and write interval notation for each compound inequality.

$$

x \geq 5 \text { or }-x \geq 4

$$

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Graph and write interval notation for each compound inequality.

$$

-x<3 \text { or } x<-6

$$

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Graph and write interval notation for each compound inequality.

$$

7>y \text { and } y \geq-3

$$

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Graph and write interval notation for each compound inequality.

$$

6>-x \geq 0

$$

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Graph and write interval notation for each compound inequality.

$$

x<7 \text { and } x \geq 3

$$

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Graph and write interval notation for each compound inequality.

$$

x \geq-3 \text { and } x<3

$$

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Graph and write interval notation for each compound inequality.

$$

t<2 \text { or } t<5

$$

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Graph and write interval notation for each compound inequality.

$$

t>4 \text { or } t>-1

$$

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Solve and graph each solution set.

$$

-7 \leq 2 a-3 \text { or } 3 a+1>7

$$

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Solve and graph each solution set.

$$

-4 \leq 3 n+5 \text { or } 2 n-3 \leq 7

$$

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Solve and graph each solution set.

$$

x+7 \leq-2 \text { or } x+7 \geq-3

$$

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Solve and graph each solution set.

$$

2 \leq f(x) \leq 8, \text { where } f(x)=3 x-1

$$

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Solve and graph each solution set.

$$

7 \geq g(x) \geq-2, \text { where } g(x)=3 x-5

$$

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Solve and graph each solution set.

$$

-21 \leq f(x)<0, \text { where } f(x)=-2 x-7

$$

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Solve and graph each solution set.

$$

4>g(t) \geq 2, \text { where } g(t)=-3 t-8

$$

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Solve and graph each solution set.

$$

f(t)<3 \text { or } f(t)>8, \text { where } f(t)=5 t+3

$$

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Solve and graph each solution set.

$$

g(x) \leq-2 \text { or } g(x) \geq 10, \text { where } g(x)=3 x-5

$$

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Solve and graph each solution set.

$$

3 a-7>-10 \text { or } 5 a+2 \leq 22

$$

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For $f(x)$ as given, use interval notation to write the domain of $f$

$$

f(x)=\frac{9}{x+8}

$$

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For $f(x)$ as given, use interval notation to write the domain of $f$

$$

f(x)=\frac{2}{x+3}

$$

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For $f(x)$ as given, use interval notation to write the domain of $f$

$$

f(x)=\frac{-8}{x}

$$

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For $f(x)$ as given, use interval notation to write the domain of $f$

$$

f(x)=\frac{x+3}{2 x-8}

$$

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For $f(x)$ as given, use interval notation to write the domain of $f$

$$

f(x)=\sqrt{x-6}

$$

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For $f(x)$ as given, use interval notation to write the domain of $f$

$$

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

$$

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For $f(x)$ as given, use interval notation to write the domain of $f$

$$

f(x)=\sqrt{2 x+7}

$$

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For $f(x)$ as given, use interval notation to write the domain of $f$

$$

f(x)=\sqrt{8-5 x}

$$

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For $f(x)$ as given, use interval notation to write the domain of $f$

$$

f(x)=\sqrt{8-2 x}

$$

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For $f(x)$ as given, use interval notation to write the domain of $f$

$$

f(x)=\sqrt{10-2 x}

$$

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Use interval notation to write each domain.

The domain of $f+g,$ if $f(x)=\sqrt{x-5}$ and $g(x)=\sqrt{\frac{1}{2} x+1}$

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Use interval notation to write each domain.

The domain of $f-g,$ if $f(x)=\sqrt{x+3}$ and $g(x)=\sqrt{2 x-1}$

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Use interval notation to write each domain.

The domain of $f \cdot g,$ if $f(x)=\sqrt{3-x}$ and $g(x)=\sqrt{3 x-2}$

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Use interval notation to write each domain.

The domain of $f+g,$ if $f(x)=\sqrt{3-4 x}$ and $g(x)=\sqrt{x+2}$

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Use interval notation to write each domain.

Why can the conjunction $2<x$ and $x<5$ be rewritten as $2<x<5,$ but the disjunction $2<x$ or $x<5$ cannot be rewritten as $2<x<5 ?$

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Use interval notation to write each domain.

Can the solution set of a disjunction be empty? Why or why not?

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What can you conclude about $a, b, c,$ and $d,$ if $[a, b] \cup[c, d]=[a, d] ?$ Why?

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What can you conclude about $a, b, c,$ and $d,$ if $[a, b] \cap[c, d]=[a, b] ?$ Why?

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Counseling. The function given by $s(t)=500 t+16,500$ can be used to estimate the number of student visits to Cornell University's counseling center $t$ years after 2000 . For what years is the number of student visits between $18,000$ and $21,000 ?$

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The function given by $P(d)=1+(d / 33)$ gives the pressure, in atmospheres (atm), at a depth of $d$ feet in the sea. For what depths $d$ is the pressure at least 1 atm and at most 7 atm?

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The function given by $f(x)=2(x+10)$ can be used to convert dress sizes $x$ in the United States to dress sizes $f(x)$ in Italy. For what dress sizes in the United States will dress sizes in Italy be between 32 and $46 ?$

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The function given by $w(t)=0.0125 t+4.525$ can be used to estimate the number of pounds of solid waste, $w(t),$ produced daily, on average, by each person in the United States, $t$ years after $2000 .$ For what years will waste production range from 4.6 lb to 4.8 lb per person per day?

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A $\$ 6.00$ toll is charged to cross the bridge from mainland Florida to Sanibel Island. A six-month reduced-fare pass, costing $\$ 50.00$ reduces the toll to $\$ 2.00 .$ A six-month unlimited-trip pass costs $\$ 300$ and allows free crossings. How many crossings in six months does it take for the reducedfare pass to be the more economical choice?

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Determine whether each sentence is true or false for all real numbers $a, b,$ and $c$

If $-b<-a,$ then $a<b$

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Determine whether each sentence is true or false for all real numbers $a, b,$ and $c$

If $a \leq c$ and $c \leq b,$ then $b>a$

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Determine whether each sentence is true or false for all real numbers $a, b,$ and $c$

If $a<c$ and $b<c,$ then $a<b$

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Determine whether each sentence is true or false for all real numbers $a, b,$ and $c$

If $-a<c$ and $-c>b,$ then $a>b$

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For $f(x)$ as given, use interval notation to write the domain of $f$

$$

f(x)=\frac{\sqrt{3-4 x}}{x+7}

$$

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For $f(x)$ as given, use interval notation to write the domain of $f$

$$

f(x)=\frac{\sqrt{5+2 x}}{x-1}

$$

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On many graphing calculators, the TEST key provides access to inequality symbols, while the LOGIC option of that same key accesses the conjunction and and the disjunction or. Thus, if $y_{1}=x>-2$ and $y_{2}=x<4,$ Exercise 55 can be checked by forming the expression $y_{3}=y_{1}$ and $y_{2} .$ The interval(s) in the solution set appears as a horizontal line 1 unit above the $x$ -axis. (Be careful to "deselect" $y_{1}$ and $y_{2}$ so that only $y_{3}$ is drawn.) Use the Test key to check Exercises $59,63,65,$ and 67

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