Question 1

Solve the problem.
-Suppose a car rental company charges  $74\$ 74$74  for the first day and  $24\$ 24$24  for each additional or partial day. Let  S(x) S(x) S(x)   represent the cost of renting a car for  xxx  days. Find the value of  S(3.5) S(3.5) S(3.5)  .

Accepted Answer

A)    $158\$ 158$158 
B)    $146\$ 146$146 
C)    $84\$ 84$84 
D)    $134\$ 134$134E) A) and B)
F) A) and C)

Question 2

Solve the problem.
-Regrind, Inc. regrinds used typewriter platens. The cost per platen is  $1.50\$ 1.50$1.50 . The fixed cost to run the grinding machine is  $232\$ 232$232  per day. If the company sells the reground platens for  $5.50\$ 5.50$5.50 , how many must be reground daily to reach the break-even point?

Accepted Answer

A)  33 platens
B)   154 platens
C)   38 platens
D)   58 platens E) All of the above
F) A) and B)

Question 3

Graph the linear function.
- f(x) =16x+1f(x) =\frac{1}{6} x+1f(x) =61​x+1

Accepted Answer

A)    
B)    C) A) and B)
D) undefined

Question 4

Give the equation of the horizontal asymptote of the rational function.
- g(x) =x−3x−4g(x) =\frac{x-3}{x-4}g(x) =x−4x−3​

Accepted Answer

A)    x=4x=4x=4 
B)    y=1y=1y=1 
C)    y=0y=0y=0 
D)    y=34\mathrm{y}=\frac{3}{4}y=43​E) B) and D)
F) B) and C)

Question 5

Solve the problem.
-The manager of a CD store has found that if the price of a CD is  p(x) =90−x8p(x) =90-\frac{x}{8}p(x) =90−8x​ , then  xCDx C DxCD  will be sold. Find an expression for the total revenue from the sale of  xxx  CDs
(hint: revenue  ===  demand  ×	imes×  price) . Use your expression to determine the maximum revenue.

Accepted Answer

A)    $32,400\$ 32,400$32,400 
B)    $8100\$ 8100$8100 
C)    $64,800\$ 64,800$64,800 
D)    $16,200\$ 16,200$16,200E) B) and C)
F) C) and D) D

Question 6

Determine whether the following rule defines $y$ as a function of $x$.
-$y=|x-3|$

Accepted Answer

A) True 
 B)False  True

Question 7

Find the appropriate linear cost or revenue function.
-Find the revenue function given the following information. Fixed cost:  $840\$ 840$840 ; marginal cost per item:  $10\$ 10$10 ; item sells for  $36\$ 36$36

Accepted Answer

A)    R(x) =10xR(x) =10 xR(x) =10x 
B)    R(x) =26x−840R(x) =26 x-840R(x) =26x−840 
C)    R(x) =36xR(x) =36 xR(x) =36x 
D)    R(x) =26xR(x) =26 xR(x) =26xE) B) and C)
F) C) and D)

Question 8

Solve the problem.
-The graph of a function is given below. Tell whether the graph could possibly be the graph of a polynomial function. If it could be the graph of a polynomial function, tell which of the following are possible degrees for the polynomial function:  3,4,5,63,4,5,63,4,5,6 .

Accepted Answer

A)   yes; 4,6
B)   yes; 4 only
C)   no
D)   yes; 6 only E) A) and B)
F) A) and C)

Question 9

Solve the problem.
-The demand for a certain type of modem is given by
 p=480−xp=480-xp=480−x 
Where  p\mathrm{p}p  is the price when  x\mathrm{x}x  units are demanded. Determine the price that will produce the maximum revenue. (Hint: First find the revenue  R(x) R(x) R(x)  , that would be obtained at a demand of  xxx  ) .

Accepted Answer

A)    $260\$ 260$260 
B)    $240\$ 240$240 
C)    $48\$ 48$48 
D)    $480\$ 480$480E) B) and C)
F) A) and B)

Question 10

Find the rule of a quadratic function whose graph has the given vertex and passes through the given point.
-vertex  (4,4) (4,4) (4,4)  ; point  (2,8) (2,8) (2,8)

Accepted Answer

A)    P(x) =2x2−8x−20P(x) =2 x^{2}-8 x-20P(x) =2x2−8x−20 
B)    P(x) =x2−4x+4P(x) =x^{2}-4 x+4P(x) =x2−4x+4 
C)    P(x) =x2−8x+20P(x) =x^{2}-8 x+20P(x) =x2−8x+20 
D)    P(x) =−x2−8x+4P(x) =-x^{2}-8 x+4P(x) =−x2−8x+4E) A) and B)
F) B) and C)

Question 11

Graph the function.
- f(x) =∣x∣−1f(x) =|x|-1f(x) =∣x∣−1

Accepted Answer

A)   
B)    
C)    
D)    E) A) and B)
F) A) and C)

Question 12

Solve the problem.
-Suppose the supply and demand for a certain videotape are given by:
  supply: p=15q2; demand: p=−15q2+36	ext { supply: } \mathrm{p}=\frac{1}{5} \mathrm{q}^{2} ; \quad 	ext { demand: } \mathrm{p}=-\frac{1}{5} \mathrm{q}^{2}+36 supply: p=51​q2; demand: p=−51​q2+36 
Where  ppp  is price and  qqq  is quantity.
Find the equilibrium demand.

Accepted Answer

A)   About 8
B)   About 11
C)   About 9
D)   About 10 E) B) and C)
F) A) and B)

Question 13

Solve the problem.
-The graph of a function is given below. Tell whether the graph could possibly be the graph of a polynomial function. If it could be the graph of a polynomial function, tell which of the following are possible degrees for the polynomial function: 3, 4, 5, 6 .

Accepted Answer

A)   yes; 5 only
B)   yes; 4 only
C)   yes; 3,5
D)   yes; 3 onlyE) B) and D)
F) None of the above

Question 14

Graph the parabola.
- y=5x2+3y=5 x^{2}+3y=5x2+3

Accepted Answer

A)    
B)    
C)    
D)    E) B) and D)
F) A) and D) D

Question 15

Solve the problem.
-A ball is thrown vertically upward at an initial speed of  40ft/sec40 \mathrm{ft} / \mathrm{sec}40ft/sec . Its height (in feet)  after  ttt  seconds is given by
 h(t) =t(40−16t) h(t) =t(40-16 t) h(t) =t(40−16t)  
After how many seconds does the ball reach its maximum height?

Accepted Answer

A)   1.25 seconds
B)   1.67 seconds
C)   2.5 seconds
D)   5 seconds E) A) and B)
F) B) and C)

Question 16

State the domain of the given function.
- f(x) =1x+6f(x) =\frac{1}{x+6}f(x) =x+61​

Accepted Answer

A)   all real numbers except 6
B)   all real numbers except -6
C)    (−6,∞) (-6, \infty) (−6,∞)  
D)    (−∞,∞) (-\infty, \infty) (−∞,∞) E) A) and B)
F) A) and C)

Question 17

Find a quadratic function that models the data.
-The table shows the population of a city in selected years. Data are in thousands rounded to the nearest hundred.

Let  x=0\mathrm{x}=0x=0  correspond to 1970 and let  f(x) \mathrm{f}(\mathrm{x}) f(x)   be the population of the city (in thousands)  in year  x\mathrm{x}x . Using the point  (0,77.9) (0,77.9) (0,77.9)   as the vertex and and the data from 1995, determine a quadratic function  f(x) =a(x−h) 2+kf(x) =a(x-h) ^{2}+kf(x) =a(x−h) 2+k  that models the data.

Accepted Answer

A)    f(x) =1.58x2+77.9f(x) =1.58 x^{2}+77.9f(x) =1.58x2+77.9 
B)    f(x) =0.079x2+77.9f(x) =0.079 x^{2}+77.9f(x) =0.079x2+77.9 
C)    f(x) =0.0632x2+77.9f(x) =0.0632 x^{2}+77.9f(x) =0.0632x2+77.9 
D)    f(x) =0.31248x2−77.9f(x) =0.31248 x^{2}-77.9f(x) =0.31248x2−77.9E) None of the above
F) B) and C)

Question 18

Graph the piecewise linear function.
- f(x) ={1,x≥−1x−3,x<−1f(x) = \begin{cases}1, & x \geq-1 \ x-3, & x<-1\end{cases}f(x) ={1,x−3,​x≥−1x<−1​

Accepted Answer

A)   
B)    
C)    
D)    E) A) and B)
F) A) and D)

Question 19

Solve the problem.
-The graph of a function is given below. Tell whether the graph could possibly be the graph of a polynomial function. If it could be the graph of a polynomial function, tell which of the following are possible degrees for the polynomial function:  3,4,5,63,4,5,63,4,5,6 .

Accepted Answer

A)   yes; 5,6
B)   yes; none
C)   yes; 6 only
D)   yes; 5 only E) A) and B)
F) None of the above

Question 20

Use the vertical line test to determine if the graph is a graph of a function.
-

Accepted Answer

A) True 
 B)False

Exam 3: Functions and Graphs

Solve the problem. -Suppose a car rental company charges $\$ 74$ for the first day and $\$ 24$ for each additional or partial day. Let $S(x)$ represent the cost of renting a car for $x$ days. Find the value of $S(3.5)$ .

Correct Answer
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Solve the problem. -Regrind, Inc. regrinds used typewriter platens. The cost per platen is $\$ 1.50$ . The fixed cost to run the grinding machine is $\$ 232$ per day. If the company sells the reground platens for $\$ 5.50$ , how many must be reground daily to reach the break-even point?

Correct Answer
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Graph the linear function. - $f(x) =\frac{1}{6} x+1$ $Graph the linear function. - f(x) =\frac{1}{6} x+1 A) B)$

Correct Answer
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Give the equation of the horizontal asymptote of the rational function. - $g(x) =\frac{x-3}{x-4}$

Correct Answer
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Solve the problem. -The manager of a CD store has found that if the price of a CD is $p(x) =90-\frac{x}{8}$ , then $x C D$ will be sold. Find an expression for the total revenue from the sale of $x$ CDs (hint: revenue $=$ demand $\times$ price) . Use your expression to determine the maximum revenue.

Correct Answer
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D

Determine whether the following rule defines $y$ as a function of $x$ . - $y=|x-3|$

Correct Answer
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True

Find the appropriate linear cost or revenue function. -Find the revenue function given the following information. Fixed cost: $\$ 840$ ; marginal cost per item: $\$ 10$ ; item sells for $\$ 36$

Correct Answer
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Solve the problem. -The graph of a function is given below. Tell whether the graph could possibly be the graph of a polynomial function. If it could be the graph of a polynomial function, tell which of the following are possible degrees for the polynomial function: $3,4,5,6$ .

Correct Answer
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Solve the problem. -The demand for a certain type of modem is given by $p=480-x$ Where $\mathrm{p}$ is the price when $\mathrm{x}$ units are demanded. Determine the price that will produce the maximum revenue. (Hint: First find the revenue $R(x)$ , that would be obtained at a demand of $x$ ) .

Correct Answer
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Find the rule of a quadratic function whose graph has the given vertex and passes through the given point. -vertex $(4,4)$ ; point $(2,8)$

Correct Answer
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Graph the function. - $f(x) =|x|-1$

Correct Answer
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Solve the problem. -Suppose the supply and demand for a certain videotape are given by: $\text { supply: } \mathrm{p}=\frac{1}{5} \mathrm{q}^{2} ; \quad \text { demand: } \mathrm{p}=-\frac{1}{5} \mathrm{q}^{2}+36$ Where $p$ is price and $q$ is quantity. Find the equilibrium demand.

Correct Answer
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Solve the problem. -The graph of a function is given below. Tell whether the graph could possibly be the graph of a polynomial function. If it could be the graph of a polynomial function, tell which of the following are possible degrees for the polynomial function: 3, 4, 5, 6 .

Correct Answer
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Graph the parabola. - $y=5 x^{2}+3$ $Graph the parabola. - y=5 x^{2}+3 A) B) C) D)$

Correct Answer
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D

Solve the problem. -A ball is thrown vertically upward at an initial speed of $40 \mathrm{ft} / \mathrm{sec}$ . Its height (in feet) after $t$ seconds is given by $h(t) =t(40-16 t)$ After how many seconds does the ball reach its maximum height?

Correct Answer
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State the domain of the given function. - $f(x) =\frac{1}{x+6}$

Correct Answer
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Correct Answer
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Graph the piecewise linear function. - $f(x) = \begin{cases}1, & x \geq-1 \\ x-3, & x<-1\end{cases}$ $Graph the piecewise linear function. - f(x) = \begin{cases}1, & x \geq-1 \\ x-3, & x<-1\end{cases} A) B) C) D)$

Correct Answer
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Solve the problem. -The graph of a function is given below. Tell whether the graph could possibly be the graph of a polynomial function. If it could be the graph of a polynomial function, tell which of the following are possible degrees for the polynomial function: $3,4,5,6$ .

Correct Answer
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Use the vertical line test to determine if the graph is a graph of a function. -

Correct Answer
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Exam 3: Functions and Graphs

Solve the problem. -Suppose a car rental company charges $74\$ 74$74 for the first day and $24\$ 24$24 for each additional or partial day. Let S(x) S(x) S(x) represent the cost of renting a car for xxx days. Find the value of S(3.5) S(3.5) S(3.5) .

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Graph the linear function. - f(x) =16x+1f(x) =\frac{1}{6} x+1f(x) =61​x+1

Correct AnswerverifiedShow Answer

Give the equation of the horizontal asymptote of the rational function. - g(x) =x−3x−4g(x) =\frac{x-3}{x-4}g(x) =x−4x−3​

Correct AnswerverifiedShow Answer

Correct AnswerverifiedD

Determine whether the following rule defines yyy as a function of xxx . - y=∣x−3∣y=|x-3|y=∣x−3∣

Correct AnswerverifiedTrue

Find the appropriate linear cost or revenue function. -Find the revenue function given the following information. Fixed cost: $840\$ 840$840 ; marginal cost per item: $10\$ 10$10 ; item sells for $36\$ 36$36

Correct AnswerverifiedShow Answer

Solve the problem. -The graph of a function is given below. Tell whether the graph could possibly be the graph of a polynomial function. If it could be the graph of a polynomial function, tell which of the following are possible degrees for the polynomial function: 3,4,5,63,4,5,63,4,5,6 .

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Find the rule of a quadratic function whose graph has the given vertex and passes through the given point. -vertex (4,4) (4,4) (4,4) ; point (2,8) (2,8) (2,8)

Correct AnswerverifiedShow Answer

Graph the function. - f(x) =∣x∣−1f(x) =|x|-1f(x) =∣x∣−1

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Solve the problem. -The graph of a function is given below. Tell whether the graph could possibly be the graph of a polynomial function. If it could be the graph of a polynomial function, tell which of the following are possible degrees for the polynomial function: 3, 4, 5, 6 .

Correct AnswerverifiedShow Answer

Graph the parabola. - y=5x2+3y=5 x^{2}+3y=5x2+3

Correct AnswerverifiedD

Solve the problem. -A ball is thrown vertically upward at an initial speed of 40ft/sec40 \mathrm{ft} / \mathrm{sec}40ft/sec . Its height (in feet) after ttt seconds is given by h(t) =t(40−16t) h(t) =t(40-16 t) h(t) =t(40−16t) After how many seconds does the ball reach its maximum height?

Correct AnswerverifiedShow Answer

State the domain of the given function. - f(x) =1x+6f(x) =\frac{1}{x+6}f(x) =x+61​

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Graph the piecewise linear function. - f(x) ={1,x≥−1x−3,x<−1f(x) = \begin{cases}1, & x \geq-1 \\ x-3, & x<-1\end{cases}f(x) ={1,x−3,​x≥−1x<−1​

Correct AnswerverifiedShow Answer

Solve the problem. -The graph of a function is given below. Tell whether the graph could possibly be the graph of a polynomial function. If it could be the graph of a polynomial function, tell which of the following are possible degrees for the polynomial function: 3,4,5,63,4,5,63,4,5,6 .

Correct AnswerverifiedShow Answer

Use the vertical line test to determine if the graph is a graph of a function. -

Correct AnswerverifiedShow Answer

Solve the problem. -Suppose a car rental company charges $\$ 74$ for the first day and $\$ 24$ for each additional or partial day. Let $S(x)$ represent the cost of renting a car for $x$ days. Find the value of $S(3.5)$ .

Correct Answer
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Correct Answer
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Graph the linear function. - $f(x) =\frac{1}{6} x+1$ $Graph the linear function. - f(x) =\frac{1}{6} x+1 A) B)$

Correct Answer
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Give the equation of the horizontal asymptote of the rational function. - $g(x) =\frac{x-3}{x-4}$

Correct Answer
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Correct Answer
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D

Determine whether the following rule defines $y$ as a function of $x$ . - $y=|x-3|$

Correct Answer
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True

Find the appropriate linear cost or revenue function. -Find the revenue function given the following information. Fixed cost: $\$ 840$ ; marginal cost per item: $\$ 10$ ; item sells for $\$ 36$

Correct Answer
verified

Solve the problem. -The graph of a function is given below. Tell whether the graph could possibly be the graph of a polynomial function. If it could be the graph of a polynomial function, tell which of the following are possible degrees for the polynomial function: $3,4,5,6$ .

Correct Answer
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Correct Answer
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Find the rule of a quadratic function whose graph has the given vertex and passes through the given point. -vertex $(4,4)$ ; point $(2,8)$

Correct Answer
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Graph the function. - $f(x) =|x|-1$

Correct Answer
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Correct Answer
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Correct Answer
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Graph the parabola. - $y=5 x^{2}+3$ $Graph the parabola. - y=5 x^{2}+3 A) B) C) D)$

Correct Answer
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D

Solve the problem. -A ball is thrown vertically upward at an initial speed of $40 \mathrm{ft} / \mathrm{sec}$ . Its height (in feet) after $t$ seconds is given by $h(t) =t(40-16 t)$ After how many seconds does the ball reach its maximum height?

Correct Answer
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State the domain of the given function. - $f(x) =\frac{1}{x+6}$

Correct Answer
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Correct Answer
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Graph the piecewise linear function. - $f(x) = \begin{cases}1, & x \geq-1 \\ x-3, & x<-1\end{cases}$ $Graph the piecewise linear function. - f(x) = \begin{cases}1, & x \geq-1 \\ x-3, & x<-1\end{cases} A) B) C) D)$

Correct Answer
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Solve the problem. -The graph of a function is given below. Tell whether the graph could possibly be the graph of a polynomial function. If it could be the graph of a polynomial function, tell which of the following are possible degrees for the polynomial function: $3,4,5,6$ .

Correct Answer
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Correct Answer
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