Question 1

Determine an appropriate viewing rectangle for the graph of the function f (x)  = 4x -  ∣3x2−10∣\left| 3 x ^ { 2 } - 10 \right|​3x2−10​  .

Accepted Answer

A)  [ - 5, 5]  ×	imes×  [ - 5, 2]
B)  [ - 50, 20]  ×	imes×  [ - 50, 10]
C)  [ - 2, 5]  ×	imes×  [ - 1, 10]
D)  [ - 10, 10]  ×	imes×  [ - 500, 500]
E)  [ - 10, 10]  ×	imes×  [ - 500, 5]F) [ - 2, 5]  ×	imes×  [ - 15, 10]G) [ - 10, 5]  ×	imes×  [ - 1, 10]H) [0, 10]  ×	imes×  [ - 2, 5] I) A) and G)
J) E) and H)

Question 2

A function has a domain [-4, 4] and a portion of its graph is shown.  (a) Complete the graph of f of its is known that f is an even function.(b) Complete the graph of f if it is known that f is an odd function.

Accepted Answer

The answer of A function has a domain [-4, 4]...

Question 3

Relative to the graph of y = x  222  , the graph of y = x  222  - 2 is changed in what way?

Accepted Answer

A)  Shifted 2 units downward
B)  Stretched horizontally by a factor of 2
C)  Shifted 2 units to the right
D)  Stretched vertically by a factor of 2
E)  Compressed horizontally by a factor of 2F) Compressed vertically by a factor of 2 G) A) and F)
H) B) and F)

Question 4

Let f(x)  = 2 - x  333  and g(x)  = 3  +++  x. Find the value of  (f∘g) (x) ( f \circ g )  ( x ) (f∘g) (x)   when x = - 5.

Accepted Answer

A)   - 510
B)   - 5
C)   - 2
D)  0
E)  5F) 10G) 127H) 130 I) E) and H)
J) All of the above

Question 5

Relative to the graph of y = x  333  , the graph of y =  12\frac { 1 } { 2 }21​  x  333  is changed in what way?

Accepted Answer

A)  Compressed horizontally by a factor of 2
B)  Shifted 2 units downward
C)  Stretched vertically by a factor of 2
D)  Stretched horizontally by a factor of 2
E)  Shifted 2 units upwardF) Compressed vertically by a factor of 2G) Shifted 2 units to the rightH) Shifted 2 units to the left I) A) and H)
J) F) and H)

Question 6

Find $f ^ { - 1 } ( x )$ if $f ( x ) = \sqrt { e ^ { 2 } + 2 }$ .

Accepted Answer

The answer of Find \(f ^ { - 1 }...

Question 7

Sketch a possible parametric curve defined by the following table of values. $$\begin{array} { | l | c c c c c c c c c | } 
\hline t & 0 & \frac { \pi } { 4 } & \frac { \pi } { 2 } & \frac { 3 \pi } { 4 } & \pi & \frac { 5 \pi } { 4 } & \frac { 3 \pi } { 2 } & \frac { 7 \pi } { 4 } & 2 \pi \
\hline x & 0 & 0.18 & 0 & - 0.53 & - 1 & - 0.88 & 0 & 1.24 & 2 \
\hline y & 0 & 0.18 & 0.5 & 0.53 & 0 & - 0.88 & - 1.5 & - 1.24 & 0 \
\hline
\end{array}$$

Accepted Answer

The answer of Sketch a possible parametric curve defined by...

Question 8

Solve for $x : e ^ { 2 x - 1 } = e ^ { \operatorname { In } 6 }$ .

Accepted Answer

The answer of Solve for \(x : e ^ {...

Question 9

Suppose pH = -log [H $+$ ]. Suppose further that for vinegar, the hydrogen ion concentration in moles per liter is given by [H $+$ ] $= 5.2 \left( 10 ^ { - 4 } \right)$ . Find the pH of the vinegar.

Accepted Answer

pH = 3.28

Question 10

Classify the function f(x)  =  π2+x2e\frac { \pi ^ { 2 } + x ^ { 2 } } { e }eπ2+x2​

Accepted Answer

A)  Power function
B)  Root function
C)  Polynomial function
D)  Rational function
E)  Algebraic functionF) Trigonometric functionG) Exponential functionH) Logarithmic function I) A) and G)
J) B) and H)

Question 11

Suppose that the position of one particle at time t is given by
x $1$ = 4 sin t, y $1$ = 2 cos t for 0 $\leq t \leq 2 \pi$ and the position of a second particle is given by
x $2$ = 2 cos t - 1, y $2$ = 4 sin t + 2 for 0 $\leq t \leq 2 \pi$ (a) How many points of intersection are there for these two paths?
(b) Are any of these collision points (that is, points where the particles are at the same place at the same time)? If so, find the collision points.

Accepted Answer

(a) 4 intersection p...

Question 12

Determine whether or not the function f (x) = $\frac { 3 x } { x - 1 }$ is one-to-one.

Accepted Answer

We see from its graph that the function ...

Question 13

Relative to the graph of y = sin x, the graph of y = 3 sin x is changed in what way?

Accepted Answer

A)  Compressed horizontally by a factor of 3
B)  Shifted 3 units to the right
C)  Compressed vertically by a factor of 3
D)  Shifted 3 units upward
E)  Shifted 3 units to the leftF) Stretched vertically by a factor of 3G) Shifted 3 units downwardH) Stretched horizontally by a factor of 3I) B) and G)
J) D) and F)

Question 14

Suppose that P(t) represents the pressure (in pounds per square inch) in a tire with a slow air leak t minutes after the leak begins. In practical terms, what is:
(a) P(20)
(b) P $- 1$ (20)

Accepted Answer

(a) The air pressure of the ti...

Question 15

Determine an appropriate viewing rectangle for the graph of the function f (x)  = 20 sin (40x)   +++  10.

Accepted Answer

A)  [ - 20, 20]  ×	imes×  [ - 20, 20]
B)  [ - 0.2, 0.2]  ×	imes×  [ - 20, 20].
C)  [ - 20, 20]  ×	imes×  [ - 0.2, 0.2]
D)  [ - 0.2, 0.2]  ×	imes×  [ - 10, 30]
E)  [ - 20, 20]  ×	imes×  [ - 20, 20] .F) [ - 0.2, 0.2]  ×	imes×  [ - 1, 1]G) [ - 10, 10]  ×	imes×  [ - 10, 10]H) [ - 1, 1]  ×	imes×  [ - 10, 10]. I) C) and H)
J) D) and E)

Question 16

Find the value of ln  e3\sqrt { e ^ { 3 } }e3​  .

Accepted Answer

A)    23\frac { 2 } { 3 }32​  
B)    e\sqrt { e }ec-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​  
C)    e3/2e ^ { 3 } / 2e3/2  
D)    32\frac { 3 } { 2 }23​  
E)    e3e ^ { 3 }e3  F)   e3e ^ { 3 }e3   −2- 2−2  G)   2e/32 e / 32e/3  H) 2/e  333  I) B) and D)
J) A) and D)

Question 17

For the exponential function f (x) = c . a $x$ + b whose graph is given below, determine the values of a, b, and c.

Accepted Answer

a = 3, b = -5, c = 2

Question 18

Determine an appropriate viewing rectangle for the graph of the function f (x)  = 6x  222  + x - 10.

Accepted Answer

A)  [ - 50, 50]  ×	imes×  [ - 50, 50]
B)  [0, 10]  ×	imes×  [0, 10]
C)  [ - 5, 10]  ×	imes×  [ - 10, 50]
D)  [ - 5, 5]  ×	imes×  [ - 5, 5]
E)  [ - 5, 5]  ×	imes×  [ - 10, 10]F) [ - 50, 10]  ×	imes×  [ - 10, 100]G) [ - 5, 50]  ×	imes×  [ - 5, 10]H) [ - 10, 10]  ×	imes×  [ - 5, 5] I) G) and H)
J) B) and H)

Question 19

Describe the curve defined by x = cos t, y = sin  222  t.

Accepted Answer

A)  Circle
B)  Semicircle
C)  Quarter-circle
D)  Parabola
E)  Portion of a parabolaF) HyperbolaG) Single branch of a hyperbolaH) Portion of branch of hyperbola I) C) and E)
J) A) and B)

Question 20

The following table contains United States population data for the years 1790-2000 at intervals of 10 years.\[\begin{array}{l}
\begin{array} { | c | c | c | } 
\hline \text { Year } & \begin{array} { c } 
\text { Years since } \
1790
\end{array} & \begin{array} { c } 
\text { U.S. population } \
\text { (millions) }
\end{array} \
\hline 1790 & 0 & 3.9 \
\hline 1800 & 10 & 5.2 \
\hline 1810 & 20 & 7.2 \
\hline 1820 & 30 & 9.6 \
\hline 1830 & 40 & 12.9 \
\hline 1840 & 50 & 17.1 \
\hline 1850 & 60 & 23.2 \
\hline 1860 & 70 & 31.4 \
\hline 1870 & 80 & 39.8 \
\hline 1880 & 90 & 50.2 \
\hline 1890 & 100 & 62.9 \
\hline
\end{array}&
\begin{array} { | c | c | c | } 
\hline \text { Year } & \begin{array} { c } 
\text { Years since } \
1790
\end{array} & \begin{array} { c } 
\text { U.S. population } \
\text { (millions) }
\end{array} \
\hline 1900 & 110 & 76.0 \
\hline 1910 & 120 & 92.0 \
\hline 1920 & 130 & 105.7 \
\hline 1930 & 140 & 122.8 \
\hline 1940 & 150 & 131.7 \
\hline 1950 & 160 & 150.7 \
\hline 1960 & 170 & 178.5 \
\hline 1970 & 180 & 202.5 \
\hline 1980 & 190 & 225.5 \
\hline 1990 & 200 & 248.7 \
\hline 2000 & 210 & 281.4 \
\hline
\end{array}
\end{array}\]
(a) Make a scatter plot for the data and use your scatter plot to determine a mathematical model for the U.S. population.(b) Use your model to predict the U.S. population in 2005.

Accepted Answer

(a) <img  loading="lazy" src="/assets/images/blured-textbook.svg" class="d-inline m-1" alt="blured image" width="139" height="30"> Answers will vary, but a quadratic ...

Exam 1: Functions and Models

Determine an appropriate viewing rectangle for the graph of the function f (x) = 4x - $\left| 3 x ^ { 2 } - 10 \right|$ .

Correct Answer
verified

A function has a domain [-4, 4] and a portion of its graph is shown. (a) Complete the graph of f of its is known that f is an even function.(b) Complete the graph of f if it is known that f is an odd function.

Correct Answer
verified

Relative to the graph of y = x $2$ , the graph of y = x $2$ - 2 is changed in what way?

Correct Answer
verified

Let f(x) = 2 - x $3$ and g(x) = 3 $+$ x. Find the value of $( f \circ g ) ( x )$ when x = - 5.

Correct Answer
verified

Relative to the graph of y = x $3$ , the graph of y = $\frac { 1 } { 2 }$ x $3$ is changed in what way?

Correct Answer
verified

Find $f ^ { - 1 } ( x )$ if $f ( x ) = \sqrt { e ^ { 2 } + 2 }$ .

Correct Answer
verified

Correct Answer
verified
11eaa8e2_1175_f5d3_96ab_edca09b5e15d_TB2033_00

Solve for $x : e ^ { 2 x - 1 } = e ^ { \operatorname { In } 6 }$ .

Correct Answer
verified

Suppose pH = -log [H $+$ ]. Suppose further that for vinegar, the hydrogen ion concentration in moles per liter is given by [H $+$ ] $= 5.2 \left( 10 ^ { - 4 } \right)$ . Find the pH of the vinegar.

Correct Answer
verified
pH = 3.28

Classify the function f(x) = $\frac { \pi ^ { 2 } + x ^ { 2 } } { e }$

Correct Answer
verified

Correct Answer
verified
(a) 4 intersection p...
View Answer

Determine whether or not the function f (x) = $\frac { 3 x } { x - 1 }$ is one-to-one.

Correct Answer
verified
We see from its graph that the function ...
View Answer

Relative to the graph of y = sin x, the graph of y = 3 sin x is changed in what way?

Correct Answer
verified

Suppose that P(t) represents the pressure (in pounds per square inch) in a tire with a slow air leak t minutes after the leak begins. In practical terms, what is: (a) P(20) (b) P $- 1$ (20)

Correct Answer
verified
(a) The air pressure of the ti...
View Answer

Determine an appropriate viewing rectangle for the graph of the function f (x) = 20 sin (40x) $+$ 10.

Correct Answer
verified

Find the value of ln $\sqrt { e ^ { 3 } }$ .

Correct Answer
verified

For the exponential function f (x) = c . a $x$ + b whose graph is given below, determine the values of a, b, and c.

Correct Answer
verified
a = 3, b = -5, c = 2

Determine an appropriate viewing rectangle for the graph of the function f (x) = 6x $2$ + x - 10.

Correct Answer
verified

Describe the curve defined by x = cos t, y = sin $2$ t.

Correct Answer
verified

Correct Answer
verified
(a) Answers will vary, but a quadratic ...
View Answer

Exam 1: Functions and Models

Determine an appropriate viewing rectangle for the graph of the function f (x) = 4x - ∣3x2−10∣\left| 3 x ^ { 2 } - 10 \right|​3x2−10​ .

Correct AnswerverifiedShow Answer

A function has a domain [-4, 4] and a portion of its graph is shown. (a) Complete the graph of f of its is known that f is an even function.(b) Complete the graph of f if it is known that f is an odd function.

Correct AnswerverifiedShow Answer

Relative to the graph of y = x 222 , the graph of y = x 222 - 2 is changed in what way?

Correct AnswerverifiedShow Answer

Let f(x) = 2 - x 333 and g(x) = 3 +++ x. Find the value of (f∘g) (x) ( f \circ g ) ( x ) (f∘g) (x) when x = - 5.

Correct AnswerverifiedShow Answer

Relative to the graph of y = x 333 , the graph of y = 12\frac { 1 } { 2 }21​ x 333 is changed in what way?

Correct AnswerverifiedShow Answer

Find f−1(x)f ^ { - 1 } ( x )f−1(x) if f(x)=e2+2f ( x ) = \sqrt { e ^ { 2 } + 2 }f(x)=e2+2​ .

Correct AnswerverifiedShow Answer

Correct Answerverified11eaa8e2_1175_f5d3_96ab_edca09b5e15d_TB2033_00

Solve for x:e2x−1=eIn⁡6x : e ^ { 2 x - 1 } = e ^ { \operatorname { In } 6 }x:e2x−1=eIn6 .

Correct AnswerverifiedShow Answer

Suppose pH = -log [H +++ ]. Suppose further that for vinegar, the hydrogen ion concentration in moles per liter is given by [H +++ ] =5.2(10−4)= 5.2 \left( 10 ^ { - 4 } \right)=5.2(10−4) . Find the pH of the vinegar.

Correct AnswerverifiedpH = 3.28

Classify the function f(x) = π2+x2e\frac { \pi ^ { 2 } + x ^ { 2 } } { e }eπ2+x2​

Correct AnswerverifiedShow Answer

Correct Answerverified(a) 4 intersection p...View AnswerShow Answer

Determine whether or not the function f (x) = 3xx−1\frac { 3 x } { x - 1 }x−13x​ is one-to-one.

Correct AnswerverifiedWe see from its graph that the function ...View AnswerShow Answer

Relative to the graph of y = sin x, the graph of y = 3 sin x is changed in what way?

Correct AnswerverifiedShow Answer

Suppose that P(t) represents the pressure (in pounds per square inch) in a tire with a slow air leak t minutes after the leak begins. In practical terms, what is: (a) P(20) (b) P −1- 1−1 (20)

Correct Answerverified(a) The air pressure of the ti...View AnswerShow Answer

Determine an appropriate viewing rectangle for the graph of the function f (x) = 20 sin (40x) +++ 10.

Correct AnswerverifiedShow Answer

Find the value of ln e3\sqrt { e ^ { 3 } }e3​ .

Correct AnswerverifiedShow Answer

For the exponential function f (x) = c . a xxx + b whose graph is given below, determine the values of a, b, and c.

Correct Answerverifieda = 3, b = -5, c = 2

Determine an appropriate viewing rectangle for the graph of the function f (x) = 6x 222 + x - 10.

Correct AnswerverifiedShow Answer

Describe the curve defined by x = cos t, y = sin 222 t.

Correct AnswerverifiedShow Answer

Correct Answerverified(a) Answers will vary, but a quadratic ...View AnswerShow Answer

Determine an appropriate viewing rectangle for the graph of the function f (x) = 4x - $\left| 3 x ^ { 2 } - 10 \right|$ .

Correct Answer
verified

Correct Answer
verified

Relative to the graph of y = x $2$ , the graph of y = x $2$ - 2 is changed in what way?

Correct Answer
verified

Let f(x) = 2 - x $3$ and g(x) = 3 $+$ x. Find the value of $( f \circ g ) ( x )$ when x = - 5.

Correct Answer
verified

Relative to the graph of y = x $3$ , the graph of y = $\frac { 1 } { 2 }$ x $3$ is changed in what way?

Correct Answer
verified

Find $f ^ { - 1 } ( x )$ if $f ( x ) = \sqrt { e ^ { 2 } + 2 }$ .

Correct Answer
verified

Correct Answer
verified
11eaa8e2_1175_f5d3_96ab_edca09b5e15d_TB2033_00

Solve for $x : e ^ { 2 x - 1 } = e ^ { \operatorname { In } 6 }$ .

Correct Answer
verified

Suppose pH = -log [H $+$ ]. Suppose further that for vinegar, the hydrogen ion concentration in moles per liter is given by [H $+$ ] $= 5.2 \left( 10 ^ { - 4 } \right)$ . Find the pH of the vinegar.

Correct Answer
verified
pH = 3.28

Classify the function f(x) = $\frac { \pi ^ { 2 } + x ^ { 2 } } { e }$

Correct Answer
verified

Correct Answer
verified
(a) 4 intersection p...
View Answer

Determine whether or not the function f (x) = $\frac { 3 x } { x - 1 }$ is one-to-one.

Correct Answer
verified
We see from its graph that the function ...
View Answer

Correct Answer
verified

Suppose that P(t) represents the pressure (in pounds per square inch) in a tire with a slow air leak t minutes after the leak begins. In practical terms, what is: (a) P(20) (b) P $- 1$ (20)

Correct Answer
verified
(a) The air pressure of the ti...
View Answer

Determine an appropriate viewing rectangle for the graph of the function f (x) = 20 sin (40x) $+$ 10.

Correct Answer
verified

Find the value of ln $\sqrt { e ^ { 3 } }$ .

Correct Answer
verified

For the exponential function f (x) = c . a $x$ + b whose graph is given below, determine the values of a, b, and c.

Correct Answer
verified
a = 3, b = -5, c = 2

Determine an appropriate viewing rectangle for the graph of the function f (x) = 6x $2$ + x - 10.

Correct Answer
verified

Describe the curve defined by x = cos t, y = sin $2$ t.

Correct Answer
verified

Correct Answer
verified
(a) Answers will vary, but a quadratic ...
View Answer