Cc Algebra Chapter 3 Answers

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iii.i Functions and Office Annotation

1.

1. ⓐyes
2. ⓑ yes (Note: If ii players had been tied for, say, 4th place, then the name would not take been a role of rank.)

6.

$y=f\left(x\right)=\frac{\sqrt[3]{x}}{2}$

9.

1. ⓐ aye, because each bank account has a unmarried balance at any given time;
2. ⓑ no, considering several bank account numbers may accept the aforementioned balance;
3. ⓒ no, because the aforementioned output may correspond to more than one input.

10.

1. ⓐ Yes, letter grade is a role of per centum class;
2. ⓑ No, information technology is not one-to-one. There are 100 different percent numbers we could get but simply about v possible letter grades, so there cannot exist but one percent number that corresponds to each letter form.

12.

No, because information technology does not pass the horizontal line test.

iii.2 Domain and Range

i.

$\{-5,0,5,\mathrm{x},15\}$

three.

$\left(-\infty ,\frac{\mathrm{one}}{2}\right)\cup \left(\frac{1}{2},\infty \right)$

4.

$\left[-\frac{5}{\mathrm{two}},\infty \right)$

5.

1. ⓐ values that are less than or equal to –2, or values that are greater than or equal to –one and less than 3
2. ⓑ $\left\{\mathrm{10}|x\le -2\text{or}-\mathrm{one}\le x<3\right\}$
3. ⓒ $(-\infty ,-\mathrm{two}]\cup [-\mathrm{one},3)$

6.

domain =[1950,2002] range = [47,000,000,89,000,000]

7.

domain: $(-\infty ,2];$ range: $(-\infty ,0]$

iii.3 Rates of Modify and Behavior of Graphs

ane.

$\frac{\$2.84-\$2.31}{\mathrm{five}\text{years}}=\frac{\$0.53}{\mathrm{five}\text{years}}=\$0.106$ per twelvemonth.

4.

The local maximum appears to occur at $(-1,28),$ and the local minimum occurs at $(5,-\mathrm{fourscore}).$ The function is increasing on $(-\infty ,-1)\cup (5,\infty )$ and decreasing on $(-1,5).$

3.iv Limerick of Functions

1.

$\begin{array}{l}\left(f\mathrm{one\; thousand}\right)\left(x\right)=f\left(\mathrm{ten}\right)g\left(\mathrm{10}\right)=\left(x-1\right)\left(x^2-1\right)=x^3-{\mathrm{ten}}^2-x+1\\ \left(f-g\right)\left(\mathrm{ten}\right)=f\left(x\right)-\mathrm{yard}\left(x\right)=\left(x-\mathrm{ane}\right)-\left(x^{\mathrm{ii}}-\mathrm{i}\right)=x-{\mathrm{ten}}^2\end{array}$

No, the functions are not the same.

2.

A gravitational force is however a force, and then $a\left(G(r)\right)$ makes sense as the acceleration of a planet at a distance r from the Sun (due to gravity), but $G\left(a(F)\right)$ does non make sense.

iii.

$f(\mathrm{chiliad}(1))=f(3)=3$ and $m(f(\mathrm{four}))=g(\mathrm{ane})=3$

4.

$k(f(2))=g(5)=\mathrm{three}$

half-dozen.

$\left[-4,0\right)\cup \left(0,\infty \right)$

7.

Possible answer:

$\begin{array}{l}k\left(x\right)=\sqrt{4+x^2}\\ h\left(x\right)=\frac{4}{3-x}\\ f=h\circ \mathrm{one\; thousand}\end{array}$

3.five Transformation of Functions

1.

$$b(t)=h(t)+\mathrm{x}=-4.9t^2+\mathrm{thirty}t+10$$

two.

The graphs of $f(x)$ and $\mathrm{grand}(\mathrm{ten})$ are shown below. The transformation is a horizontal shift. The function is shifted to the left past two units.

iv.

$\mathrm{one\; thousand}\left(\mathrm{ten}\right)=\frac{1}{x-\mathrm{i}}+\mathrm{one}$

6.

1. ⓐ

   $g(x)=-f(x)$

   $x$	-two	0	two	four
   $g(\mathrm{10})$	$-5$	$-10$	$-15$	$-20$

2. ⓑ

   $h(\mathrm{10})=f(\text{−}x)$

   $x$	-2	0	2	4
   $h(\mathrm{10})$	xv	10	five	unknown

vii.

Detect: $\mathrm{one\; thousand}(x)=f(-x)$ looks the same as $f(\mathrm{10})$ .

9.

$x$	2	four	half-dozen	8
$g(x)$	ix	12	15	0

11.

$\mathrm{thou}(x)=f\left(\frac{\mathrm{i}}{3}x\right)$ so using the foursquare root part we get $\mathrm{thousand}(x)=\sqrt{\frac{\mathrm{ane}}{3}x}$

iii.6 Absolute Value Functions

1.

using the variable $p$ for passing, $\left|p-80\right|\le 20$

two.

$f(x)=-\left|\mathrm{ten}+\mathrm{ii}\right|+3$

3.7 Inverse Functions

four.

The domain of role $f^{-1}$ is $(-\infty \text{,}-\mathrm{ii})$ and the range of function $f^{-1}$ is $(1,\infty ).$

five.

1. ⓐ $f(60)=50.$ In threescore minutes, fifty miles are traveled.
2. ⓑ $f^{-1}(60)=70.$ To travel 60 miles, it will take seventy minutes.

8.

$f^{-\mathrm{ane}}(x)={\left(\mathrm{ii}-\mathrm{ten}\right)}^2;\text{domain}\text{of}f:\left[0,\infty \right);\text{domain}\text{of}{f}^{-1}:\left(-\infty ,2\right]$

three.1 Department Exercises

1.

A relation is a set of ordered pairs. A part is a special kind of relation in which no two ordered pairs have the same first coordinate.

3.

When a vertical line intersects the graph of a relation more than than one time, that indicates that for that input in that location is more than i output. At any particular input value, at that place tin can be only one output if the relation is to be a role.

5.

When a horizontal line intersects the graph of a function more than in one case, that indicates that for that output at that place is more than ane input. A function is one-to-1 if each output corresponds to only one input.

27.

$f(-\mathrm{iii})=-\mathrm{eleven};$
$f(\mathrm{two})=-1;$
$f(-a)=-2a-\mathrm{five};$
$-f(a)=-2a+5;$
$f(a+h)=2a+\mathrm{ii}h-5$

29.

$f(-3)=\sqrt{5}+5;$
$f(2)=5;$
$f(-a)=\sqrt{2+a}+5;$
$-f(a)=-\sqrt{2-a}-5;$
$f(a+h)=\sqrt{\mathrm{ii}-a-h}+5$

31.

$f(-\mathrm{iii})=\mathrm{ii};$ $f(2)=\mathrm{i}-3=-\mathrm{ii};$
$f(-a)=|-a-\mathrm{ane}|-|-a+\mathrm{i}|;$
$-f(a)=-|a-1|+|a+1|;$
$f(a+h)=|a+h-1|-|a+h+1|$

33.

$\frac{g(x)-g(a)}{x-a}=x+a+2,\mathrm{10}\ne a$

35.

a. $f(-\mathrm{ii})=14;$ b. $\mathrm{ten}=3$

37.

a. $f(5)=\mathrm{x};$ b. $\mathrm{10}=-\mathrm{i}$ or $x=\mathrm{four}$

39.

1. ⓐ $f(t)=\mathrm{half\; dozen}-\frac{2}{3}t;$
2. ⓑ $f(-\mathrm{three})=\mathrm{eight};$
3. ⓒ $t=6$

53.

1. ⓐ $f(0)=1;$
2. ⓑ $f(\mathrm{ten})=-3,x=-2$ or $x=2$

55.

not a function and so it is too not a 1-to-one office

59.

function, but not one-to-ane

67.

$f(x)=\mathrm{one},\mathrm{10}=2$

69.

$\begin{array}{ccccc}f(-\mathrm{two})=14;& f(-1)=11;& f(0)=\mathrm{eight};& f(\mathrm{one})=5;& f(2)=2\end{array}$

71.

$\begin{array}{ccccc}f(-2)=4;& f(-1)=4.414;& f(0)=\mathrm{iv.732};& f(1)=5;& f(2)=5.236\end{array}$

73.

$\begin{array}{ccccc}f(-\mathrm{ii})=\frac{1}{9};& f(-1)=\frac{1}{3};& f(0)=1;& f(\mathrm{i})=3;& f(2)=\mathrm{nine}\end{array}$

77.

$[0,\text{100}]$

79.

$[-0.001,\text{0}\text{.001}]$

81.

$[-\mathrm{i},000,000,\text{1,000,000}]$

83.

$[0,\text{ten}]$

85.

$[\mathrm{-0.i},\text{0.1}]$

87.

$[-100,\text{100}]$

89.

1. ⓐ $g(5000)=50;$
2. ⓑ The number of cubic yards of dirt required for a garden of 100 square feet is 1.

91.

1. ⓐ The top of a rocket higher up ground afterward 1 second is 200 ft.
2. ⓑ The height of a rocket above ground after 2 seconds is 350 ft.

3.2 Section Exercises

1.

The domain of a function depends upon what values of the independent variable make the function undefined or imaginary.

3.

There is no restriction on $\mathrm{10}$ for $f(x)=\sqrt[\mathrm{iii}]{\mathrm{10}}$ because you can accept the cube root of any real number. Then the domain is all real numbers, $(-\infty ,\infty ).$ When dealing with the ready of existent numbers, you cannot take the foursquare root of negative numbers. And then $x$ -values are restricted for $f(x)=\sqrt[]{\mathrm{ten}}$ to nonnegative numbers and the domain is $[0,\infty ).$

v.

Graph each formula of the piecewise function over its corresponding domain. Apply the same scale for the $\mathrm{ten}$ -axis and $y$ -axis for each graph. Indicate inclusive endpoints with a solid circle and exclusive endpoints with an open circumvolve. Apply an arrow to indicate $-\infty$ or $\infty .$ Combine the graphs to find the graph of the piecewise role.

15.

$(-\infty ,-\frac{1}{\mathrm{ii}})\cup (-\frac{1}{2},\infty )$

17.

$(-\infty ,-11)\cup (-\mathrm{xi},2)\cup (\mathrm{ii},\infty )$

19.

$(-\infty ,-\mathrm{iii})\cup (-\mathrm{three},5)\cup (5,\infty )$

25.

$\left(-\infty ,-9\right)\cup \left(-9,\mathrm{ix}\right)\cup \left(9,\infty \right)$

27.

domain: $(2,\mathrm{viii}],$ range $[\mathrm{six},8)$

29.

domain: $[-\mathrm{iv},\text{4],}$ range: $[0,\text{two]}$

31.

domain: $[-5,\mathrm{three}),$ range: $\left[0,2\right]$

33.

domain: $(-\infty ,1],$ range: $[0,\infty )$

35.

domain: $\left[-\mathrm{half\; dozen},-\frac{\mathrm{i}}{\mathrm{half\; dozen}}\right]\cup \left[\frac{1}{6},6\right];$ range: $\left[-\mathrm{six},-\frac{1}{\mathrm{half-dozen}}\right]\cup \left[\frac{1}{6},6\right]$

37.

domain: $[-3,\infty );$ range: $[0,\infty )$

39.

domain: $(-\infty ,\infty )$

41.

domain: $(-\infty ,\infty )$

43.

domain: $(-\infty ,\infty )$

45.

domain: $(-\infty ,\infty )$

47.

$\begin{array}{cccc}f(-3)=1;& f(-\mathrm{ii})=0;& f(-\mathrm{one})=0;& f(0)=0\end{array}$

49.

$\begin{array}{cccc}f(-1)=-\mathrm{iv};& f(0)=6;& f(2)=20;& f(4)=34\end{array}$

51.

$\begin{array}{cccc}f(-\mathrm{one})=-5;& f(0)=\mathrm{three};& f(\mathrm{two})=3;& f(4)=16\end{array}$

53.

domain: $(-\infty ,\mathrm{ane})\cup (1,\infty )$

55.

window: $[-0.5,-\mathrm{0.i}];$ range: $[4,100]$

window: $[0.1,\mathrm{0.v}];$ range: $[\mathrm{iv},100]$

59.

Many answers. 1 part is $f(x)=\frac{\mathrm{i}}{\sqrt{\mathrm{10}-\mathrm{two}}}.$

61.

1. ⓐ The fixed toll is $500.
2. ⓑ The cost of making 25 items is $750.
3. ⓒ The domain is [0, 100] and the range is [500, 1500].

3.3 Section Exercises

ane.

Yes, the average charge per unit of change of all linear functions is constant.

3.

The accented maximum and minimum chronicle to the entire graph, whereas the local extrema relate but to a specific region effectually an open up interval.

11.

$\frac{-1}{13\left(13+h\right)}$

13.

$\mathrm{three}{h}^2+\mathrm{nine}h+\mathrm{ix}$

19.

increasing on $\left(-\infty ,-2.5\right)\cup \left(1,\infty \right),$ decreasing on $(-\mathrm{2.five},1)$

21.

increasing on $\left(-\infty ,1\right)\cup \left(\mathrm{three},\mathrm{four}\right),$ decreasing on $\left(1,3\right)\cup \left(4,\infty \right)$

23.

local maximum: $(-\mathrm{three},60),$ local minimum: $(\mathrm{iii},-60)$

25.

absolute maximum at approximately $(\mathrm{seven},150),$ absolute minimum at approximately $(\mathrm{-7.five},\mathrm{-220})$

35.

Local minimum at $(3,-22),$ decreasing on $(-\infty ,3),$ increasing on $(3,\infty )$

37.

Local minimum at $(-2,-2),$ decreasing on $(-\mathrm{three},-2),$ increasing on $(-2,\infty )$

39.

Local maximum at $(-0.5,\mathrm{six}),$ local minima at $(-\mathrm{three.25},-47)$ and $(2.1,-32),$ decreasing on $(-\infty ,-\mathrm{three.25})$ and $(-0.5,2.1),$ increasing on $(-3.25,-0.5)$ and $(\mathrm{2.one},\infty )$

45.

ii.7 gallons per minute

47.

approximately –0.6 milligrams per day

three.iv Section Exercises

one.

Find the numbers that make the role in the denominator $g$ equal to zero, and check for whatever other domain restrictions on $f$ and $\mathrm{1000},$ such every bit an even-indexed root or zeros in the denominator.

3.

Yes. Sample answer: Allow $f(x)=\mathrm{10}+\mathrm{ane}\text{and}\mathrm{thou}(x)=x-1.$ And so $f(g(\mathrm{ten}))=f(x-\mathrm{one})=(\mathrm{ten}-\mathrm{i})+\mathrm{ane}=\mathrm{10}$ and $g(f(x))=\mathrm{thou}(x+1)=(x+1)-1=x.$ So $f\circ m=\mathrm{thou}\circ f.$

5.

$(f+\mathrm{thou})\left(x\right)=\mathrm{two}x+\mathrm{half-dozen},$ domain: $(-\infty ,\infty )$

$(f-g)\left(x\right)=2{\mathrm{10}}^2+2\mathrm{10}-6,$ domain: $(-\infty ,\infty )$

$(fg)\left(\mathrm{10}\right)=-{\mathrm{ten}}^4-2x^3+\mathrm{six}{x}^2+12x,$ domain: $(-\infty ,\infty )$

$\left(\frac{f}{g}\right)\left(x\right)=\frac{{\mathrm{ten}}^2+\mathrm{ii}x}{6-x^{\mathrm{two}}},$ domain: $(-\infty ,-\sqrt{6})\cup (-\sqrt{6},\sqrt{\mathrm{vi}})\cup (\sqrt{\mathrm{vi}},\infty )$

vii.

$(f+\mathrm{one\; thousand})\left(x\right)=\frac{\mathrm{four}{x}^{\mathrm{three}}+8x^2+\mathrm{one}}{\mathrm{two}x},$ domain: $(-\infty ,0)\cup (0,\infty )$

$(f-g)\left(x\right)=\frac{\mathrm{four}{x}^3+\mathrm{viii}{\mathrm{10}}^2-\mathrm{one}}{2x},$ domain: $(-\infty ,0)\cup (0,\infty )$

$(fg)\left(\mathrm{10}\right)=\mathrm{10}+\mathrm{two},$ domain: $(-\infty ,0)\cup (0,\infty )$

$\left(\frac{f}{\mathrm{thou}}\right)\left(x\right)=4{\mathrm{10}}^3+8x^{\mathrm{ii}},$ domain: $(-\infty ,0)\cup (0,\infty )$

9.

$(f+g)(x)=3x^2+\sqrt{x-5},$ domain: $[5,\infty )$

$(f-g)(\mathrm{ten})=\mathrm{iii}{\mathrm{ten}}^2-\sqrt{\mathrm{ten}-5},$ domain: $[5,\infty )$

$(f\mathrm{yard})(x)=3{\mathrm{ten}}^2\sqrt{\mathrm{10}-5},$ domain: $[5,\infty )$

$\left(\frac{f}{g}\right)(\mathrm{10})=\frac{3{\mathrm{ten}}^2}{\sqrt{\mathrm{10}-5}},$ domain: $(5,\infty )$

xi.

1. ⓐ 3
2. ⓑ $f\left(g\left(x\right)\right)=2{\left(3\mathrm{10}-5\right)}^2+\mathrm{ane}$
3. ⓒ $f\left(g\left(x\right)\right)=6x^2-2$
4. ⓓ $\left(k\circ g\right)(\mathrm{ten})=3(3\mathrm{ten}-5)-\mathrm{five}=9x-20$
5. ⓔ $\left(f\circ f\right)\left(-2\right)=163$

13.

$f(\mathrm{one\; thousand}(x))=\sqrt{x^2+3}+\mathrm{ii},g(f(x))=x+4\sqrt{\mathrm{ten}}+\mathrm{seven}$

xv.

$f(\mathrm{thousand}(x))=\sqrt[3]{\frac{\mathrm{ten}+\mathrm{ane}}{x^3}}=\frac{\sqrt[3]{x+\mathrm{i}}}{x},\mathrm{one\; thousand}(f(x))=\frac{\sqrt[3]{x}+\mathrm{one}}{x}$

17.

$\left(f\circ g\right)(x)=\frac{\mathrm{ane}}{\frac{\mathrm{ii}}{\mathrm{ten}}+4-\mathrm{four}}=\frac{\mathrm{ten}}{2},\left(m\circ f\right)(x)=\mathrm{two}\mathrm{ten}-4$

xix.

$f(\mathrm{chiliad}(h(\mathrm{10})))={\left(\frac{\mathrm{ane}}{x+3}\right)}^2+\mathrm{i}$

21.

1. ⓐ $(m\circ f)(\mathrm{ten})=-\frac{3}{\sqrt{2-4x}}$
2. ⓑ $\left(-\infty ,\frac{\mathrm{i}}{2}\right)$

23.

1. ⓐ $(0,\mathrm{ii})\cup (2,\infty );$
2. ⓑ $(-\infty ,-2)\cup (2,\infty );$
3. ⓒ $(0,\infty )$

27.

sample: $\begin{array}{l}f(x)=x^{\mathrm{iii}}\\ \mathrm{yard}(\mathrm{10})=x-\mathrm{five}\end{array}$

29.

sample: $\begin{array}{l}f(\mathrm{ten})=\frac{4}{x}\hfill \\ g(x)={(x+2)}^{\mathrm{two}}\hfill \end{array}$

31.

sample: $\begin{array}{l}f(x)=\sqrt[3]{\mathrm{ten}}\\ g(x)=\frac{1}{\mathrm{ii}x-3}\end{array}$

33.

sample: $\begin{array}{l}f(\mathrm{ten})=\sqrt[\mathrm{iv}]{x}\\ g(x)=\frac{3\mathrm{10}-2}{x+5}\end{array}$

35.

sample: $\begin{array}{l}f(x)=\sqrt{\mathrm{10}}\\ g(x)=2x+6\end{array}$

37.

sample: $\begin{array}{l}f(x)=\sqrt[3]{\mathrm{10}}\\ g(x)=(x-\mathrm{i})\end{array}$

39.

sample: $\begin{array}{l}f(x)={\mathrm{ten}}^3\\ \mathrm{chiliad}(x)=\frac{1}{x-2}\end{array}$

41.

sample: $\begin{array}{l}f(\mathrm{ten})=\sqrt{\mathrm{10}}\\ \mathrm{thou}(x)=\frac{2x-1}{3x+4}\end{array}$

73.

$f(g(0))=27,g\left(f(0)\right)=-94$

75.

$f(\mathrm{thousand}(0))=\frac{1}{\mathrm{five}},g(f(0))=\mathrm{five}$

77.

$18x^{\mathrm{two}}+60x+51$

79.

$g\circ g(x)=9\mathrm{10}+20$

87.

$(f\circ \mathrm{1000})(\mathrm{vi})=\mathrm{six}$ ; $(g\circ f)(6)=\mathrm{vi}$

89.

$(f\circ g)(11)=11,(g\circ f)(11)=\mathrm{eleven}$

93.

$A(t)=\pi {\left(25\sqrt{t+2}\right)}^2$ and $A(2)=\pi {\left(25\sqrt{4}\right)}^2=2500\pi$ square inches

95.

$A(\mathrm{five})=\pi {\left(\mathrm{ii}(5)+1\right)}^{\mathrm{ii}}=121\pi$ foursquare units

97.

1. ⓐ $N(T(t))=23{(5t+\mathrm{1.five})}^2-56(5t+\mathrm{i.5})+1$
2. ⓑ 3.38 hours

three.5 Section Exercises

1.

A horizontal shift results when a constant is added to or subtracted from the input. A vertical shifts results when a constant is added to or subtracted from the output.

three.

A horizontal compression results when a constant greater than 1 is multiplied by the input. A vertical compression results when a constant between 0 and 1 is multiplied by the output.

5.

For a part $f,$ substitute $(-x)$ for $(x)$ in $f(x).$ Simplify. If the resulting office is the same as the original role, $f(-\mathrm{ten})=f(x),$ then the function is even. If the resulting office is the opposite of the original part, $f(-x)=-f(x),$ then the original role is odd. If the role is not the same or the opposite, then the function is neither odd nor even.

7.

$g(\mathrm{10})=|\mathrm{ten}-1|-\mathrm{iii}$

9.

$g(x)=\frac{1}{{(x+4)}^2}+\mathrm{two}$

11.

The graph of $f(x+43)$ is a horizontal shift to the left 43 units of the graph of $f.$

thirteen.

The graph of $f(x-4)$ is a horizontal shift to the right iv units of the graph of $f.$

15.

The graph of $f(x)+8$ is a vertical shift upwardly 8 units of the graph of $f.$

17.

The graph of $f(\mathrm{10})-7$ is a vertical shift downwardly 7 units of the graph of $f.$

nineteen.

The graph of $f(x+\mathrm{iv})-\mathrm{one}$ is a horizontal shift to the left 4 units and a vertical shift down one unit of the graph of $f.$

21.

decreasing on $(-\infty ,-3)$ and increasing on $(-3,\infty )$

23.

decreasing on $(0,\infty )$

31.

$\mathrm{chiliad}(\mathrm{ten})=f(x-\mathrm{i}),h(x)=f(\mathrm{10})+\mathrm{i}$

33.

$f(x)=|\mathrm{ten}-\mathrm{iii}|-2$

35.

$f(x)=\sqrt{x+3}-\mathrm{ane}$

37.

$f(x)={(\mathrm{ten}-2)}^2$

39.

$f(x)=|x+3|-2$

43.

$f(x)=-{(x+1)}^{\mathrm{ii}}+\mathrm{two}$

45.

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

53.

The graph of $\mathrm{grand}$ is a vertical reflection (beyond the $x$ -centrality) of the graph of $f.$

55.

The graph of $m$ is a vertical stretch by a factor of 4 of the graph of $f.$

57.

The graph of $\mathrm{1000}$ is a horizontal compression past a factor of $\frac{1}{5}$ of the graph of $f.$

59.

The graph of $g$ is a horizontal stretch by a factor of 3 of the graph of $f.$

61.

The graph of $\mathrm{grand}$ is a horizontal reflection beyond the $y$ -axis and a vertical stretch past a factor of iii of the graph of $f.$

63.

$g(x)=|-\mathrm{iv}x|$

65.

$g(x)=\frac{1}{\mathrm{iii}{(x+\mathrm{ii})}^{\mathrm{ii}}}-\mathrm{three}$

67.

$g(x)=\frac{\mathrm{one}}{\mathrm{two}}{(\mathrm{10}-5)}^{\mathrm{ii}}+1$

69.

The graph of the office $f(x)=x^2$ is shifted to the left 1 unit, stretched vertically past a factor of iv, and shifted downwardly v units.

71.

The graph of $f(x)=\left|\mathrm{10}\right|$ is stretched vertically by a factor of 2, shifted horizontally 4 units to the right, reflected across the horizontal axis, and then shifted vertically 3 units up.

73.

The graph of the function $f(\mathrm{10})={\mathrm{ten}}^3$ is compressed vertically past a factor of $\frac{\mathrm{one}}{\mathrm{two}}.$

75.

The graph of the function is stretched horizontally by a cistron of 3 and then shifted vertically downward past iii units.

77.

The graph of $f(\mathrm{10})=\sqrt{\mathrm{10}}$ is shifted right 4 units and then reflected across the vertical line $x=\mathrm{four.}$

three.6 Section Exercises

1.

Isolate the accented value term then that the equation is of the form $\left|A\right|=B.$ Class one equation by setting the expression inside the absolute value symbol, $A,$ equal to the expression on the other side of the equation, $B.$ Form a second equation by setting $A$ equal to the contrary of the expression on the other side of the equation, $-B.$ Solve each equation for the variable.

iii.

The graph of the accented value office does not cantankerous the $\mathrm{10}$ -axis, so the graph is either completely higher up or completely beneath the $\mathrm{10}$ -axis.

5.

The distance from x to 8 can be represented using the absolute value statement: ∣ x − 8 ∣ = 4.

nine.

There are no x-intercepts.

13.

$(0,-4),(\mathrm{four},0),(-\mathrm{two},0)$

15.

$(0,7),(25,0),(-7,0)$

33.

range: $[–400,100]$

37.

There is no solution for $a$ that will keep the function from having a $y$ -intercept. The absolute value function e'er crosses the $y$ -intercept when $\mathrm{10}=0.$

39.

$\left|p-0.08\right|\le 0.015$

41.

$\left|x-5.0\right|\le 0.01$

three.7 Section Exercises

1.

Each output of a function must have exactly one output for the function to be one-to-one. If any horizontal line crosses the graph of a function more than than once, that means that $y$ -values repeat and the function is not one-to-i. If no horizontal line crosses the graph of the function more than than once, so no $y$ -values repeat and the function is ane-to-i.

3.

Yes. For example, $f(x)=\frac{1}{x}$ is its ain inverse.

v.

Given a function $y=f(\mathrm{ten}),$ solve for $x$ in terms of $y.$ Interchange the $\mathrm{ten}$ and $y.$ Solve the new equation for $y.$ The expression for $y$ is the changed, $y=f^{-1}(\mathrm{10}).$

7.

$f^{-\mathrm{one}}(x)=x-3$

nine.

$f^{-1}(\mathrm{10})=2-x$

eleven.

$f^{-1}(x)=\frac{-\mathrm{ii}\mathrm{10}}{x-1}$

13.

domain of $f(x):[-7,\infty );f^{-1}(x)=\sqrt{x}-7$

15.

domain of $f(x):[0,\infty );f^{-1}(\mathrm{ten})=\sqrt{x+5}$

xvi.

a. $f(g(\mathrm{ten}))=x$ and $\mathrm{grand}(f(\mathrm{10}))=\mathrm{ten}.$ b. This tells united states of america that $f$ and $g$ are inverse functions

17.

$f(\mathrm{thou}(x))=\mathrm{10},\mathrm{chiliad}(f(x))=x$

41.

$x$	1	4	7	12	xvi
$f^{-1}(x)$	3	six	9	13	14

43.

$f^{-1}(\mathrm{ten})={(1+x)}^{1/3}$

45.

$f^{-1}(x)=\frac{\mathrm{five}}{\mathrm{ix}}\left(x-32\right).$ Given the Fahrenheit temperature, $x,$ this formula allows you to calculate the Celsius temperature.

47.

$t(d)=\frac{d}{50},$ $t(180)=\frac{180}{50}.$ The time for the car to travel 180 miles is iii.six hours.

Review Exercises

five.

$f(-\mathrm{iii})=-27;$ $f(2)=-\mathrm{ii};$ $f(-a)=-\mathrm{ii}{a}^{\mathrm{ii}}-\mathrm{iii}a;$
$-f(a)=2a^{\mathrm{two}}-3a;$ $f(a+h)=-\mathrm{ii}{a}^2+3a-4ah+3h-2h^{\mathrm{two}}$

17.

$x=-1.8$ or $\text{or}x=\mathrm{1.viii}$

nineteen.

$\frac{-64+\mathrm{lxxx}a-16a^2}{-1+a}=-16a+64$

21.

$\left(-\infty ,-2\right)\cup \left(-2,\mathrm{half-dozen}\right)\cup \left(\mathrm{half\; dozen},\infty \right)$

27.

increasing $\left(2,\infty \right);$ decreasing $(-\infty ,2)$

29.

increasing $\left(-3,1\right);$ constant $(-\infty ,-\mathrm{three})\cup \left(\mathrm{one},\infty \right)$

31.

local minimum $\left(-2,-3\right);$ local maximum $\left(1,3\right)$

33.

$\left(-\mathrm{1.viii},10\right)$

35.

$\left(f\circ m\right)(x)=17-18x;\left(g\circ f\right)(\mathrm{10})=-7-\mathrm{eighteen}x$

37.

$\left(f\circ g\right)(\mathrm{ten})=\sqrt{\frac{1}{\mathrm{ten}}+2};\left(g\circ f\right)(x)=\frac{1}{\sqrt{x+\mathrm{ii}}}$

39.

$(f\circ g)(x)=\frac{1+x}{1+4x},\mathrm{ten}\ne 0,x\ne -\frac{1}{4}$

41.

$\left(f\circ g\right)(\mathrm{10})=\frac{1}{\sqrt{x}},x>0$

43.

sample: $g(\mathrm{10})=\frac{2x-\mathrm{one}}{3x+4};f(x)=\sqrt{x}$

55.

$f(\mathrm{ten})=\left|x-3\right|$

63.

$f(x)=\frac{1}{2}\left|x+2\right|+1$

65.

$f(x)=-\mathrm{three}\left|x-3\right|+3$

69.

$f^{-\mathrm{i}}(x)=\frac{x-9}{10}$

71.

$f^{-1}(x)=\sqrt{x-1}$

73.

The function is one-to-i.

Practice Examination

1.

The relation is a function.

v.

The graph is a parabola and the graph fails the horizontal line test.

xix.

$f^{-\mathrm{ane}}(x)=\frac{x+5}{3}$

21.

$(-\infty ,-1.1)\text{and}(\mathrm{i.i},\infty )$

23.

$\left(\mathrm{one.ane},-0.9\right)$

27.

$f(\mathrm{10})=\{\begin{array}{c}\left|x\right|\text{if}x\le 2\\ 3\text{if}x>\mathrm{two}\end{array}$

33.

$f^{-\mathrm{ane}}(x)=-\frac{x-11}{2}$

Cc Algebra Chapter 3 Answers,

Source: https://openstax.org/books/college-algebra/pages/chapter-3

Posted by: pucciospirly98.blogspot.com

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