Question 1

Determine the domain and the range of the function.
-$$f ( x ) = x ^ { 2 } + 8 x + 7$$

Accepted Answer

A)  domain: range: $\{ x \mid x \geq 4 \}$
 range: $\{ y \mid y \geq 9 \}$ 
B)  domain: range: $\{ x \mid x \geq 4 \}$
range: $\{ y \mid y \geq - 9 \}$ 
C)  domain: all real numbers
range: $\{ y \mid y \geq - 9 \}$ 
D)  domain: all real numbers 
range: $\{ \mathrm { y } \mid \mathrm { y } \geq 9 \}$ 
A)  domain: range: $\{ x \mid x \geq 4 \}$
 range: $\{ y \mid y \geq 9 \}$ 
B)  domain: range: $\{ x \mid x \geq 4 \}$
range: $\{ y \mid y \geq - 9 \}$ 
C)  domain: all real numbers
range: $\{ y \mid y \geq - 9 \}$ 
D)  domain: all real numbers 
range: $\{ \mathrm { y } \mid \mathrm { y } \geq 9 \}$

Question 2

Choose the one alternative that best completes the statement or answers the question.
-The quadratic function $f ( x ) = 0.0040 x ^ { 2 } - 0.43 x + 36.98$ models the median, or average, age, $y$, at which U.S. men were first married x years after 1900 . In which year was this average age at a minimum? (Round to the nearest year.) What was the average age at first marriage for that year? (Round to the nearest tenth.)

Accepted Answer

A)  1953,36 years old 
B)  $1936,48.5$ years old 
C)  $1954,25.4$ years old 
D)  $1954,48.5$ years old 
A)  1953,36 years old 
B)  $1936,48.5$ years old 
C)  $1954,25.4$ years old 
D)  $1954,48.5$ years old

Question 3

Find the vertex and axis of symmetry of the graph of the function.
-$$f ( x ) = x ^ { 2 } + 2 x - 3$$

Accepted Answer

A)  (-1, -4); x = -1 
B)  (1, 4); x = 1 
C)  (1, -4); x = 1 
D)  (-1, 4); x = -1 
A)  (-1, -4); x = -1 
B)  (1, 4); x = 1 
C)  (1, -4); x = 1 
D)  (-1, 4); x = -1

Question 4

Find the real zeros of the function. List the x-intercepts of the graph of the function.
-$$G ( x ) = x ^ { 4 } - 23 x ^ { 2 } - 50$$

Accepted Answer

A)  $x = - 5 , x = 5$ 
B)  $x = - 25 , x = 2$ 
C)  $x = - \sqrt { 2 } , x = \sqrt { 2 }$ 
D)  no real solution 
A)  $x = - 5 , x = 5$ 
B)  $x = - 25 , x = 2$ 
C)  $x = - \sqrt { 2 } , x = \sqrt { 2 }$ 
D)  no real solution

Question 5

Solve the problem.
-The price $p$ (in dollars) and the quantity $x$ sold of a certain product obey the demand equation $x = - 6 p + 120 , \quad 0 \leq p \leq 20$.
What quantity $x$ maximizes revenue? What is the maximum revenue?

Accepted Answer

A)  $60 ; \$ 600$ 
B)  90; $\$ 450$ 
C)  $30 ; \$ 450$ 
D)  $120 ; \$ 600$ 
A)  $60 ; \$ 600$ 
B)  90; $\$ 450$ 
C)  $30 ; \$ 450$ 
D)  $120 ; \$ 600$

Question 6

Determine the average rate of change for the function.
-h(x) = -4x + 10

Accepted Answer

A)  10 
B)  -10 
C)  -4 
D)  4 
A)  10 
B)  -10 
C)  -4 
D)  4

Question 7

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary.
-$\begin{array}{l|ccccc}
\mathrm{x} & 2 & 4 & 6 & 8 & 10 \
\hline \mathrm{y} & 15 & 37 & 60 & 75 & 94
\end{array}$

Accepted Answer

A)  $y = 9 x - 3$ 
B)  $y = 9.8 x - 2.6$ 
C)  $y = 9.2 x - 2.1$ 
D)  $y = 10 x - 3$ 
A)  $y = 9 x - 3$ 
B)  $y = 9.8 x - 2.6$ 
C)  $y = 9.2 x - 2.1$ 
D)  $y = 10 x - 3$

Question 8

Solve the equation.
-$$| x | = 7$$

Accepted Answer

A)  $\{ - 7,7 \}$ 
B)  $\{ - 7 \}$ 
C)  $\{ 7 \}$ 
D)  $\{ 49 \}$ 
A)  $\{ - 7,7 \}$ 
B)  $\{ - 7 \}$ 
C)  $\{ 7 \}$ 
D)  $\{ 49 \}$

Question 9

Find the real zeros, if any, of each quadratic function using the quadratic formula. List the x-intercepts, if any, of the
graph of the function.
-$$h ( x ) = x ^ { 2 } - 4 x + 20$$

Accepted Answer

A)  $x = - 2 , x = 4$ 
B)  $x = 6 , x = - 2$ 
C)  $x = 4 , x = - 8$ 
D)  No real zeros or x-intercepts 
A)  $x = - 2 , x = 4$ 
B)  $x = 6 , x = - 2$ 
C)  $x = 4 , x = - 8$ 
D)  No real zeros or x-intercepts

Question 10

Solve the problem.
-A lumber yard has fixed costs of $4,726.80 per day and variable costs of $0.1 per board-foot produced. Lumber sells for $1.90 per board-foot. How many board-feet must be produced and sold daily to break even?

Accepted Answer

A)  2,363 board-feet 
B)  47,268 board-feet 
C)  1,750 board-feet 
D)  2,626 board-feet 
A)  2,363 board-feet 
B)  47,268 board-feet 
C)  1,750 board-feet 
D)  2,626 board-feet

Question 11

Plot a scatter diagram.
-$$\begin{array} { l | c c c c c c c c c } 
\mathrm { x } & 15 & 21 & 36 & 46 & 58 & 70 & 71 & 84 & 95 \
\hline \mathrm { y } & 10 & 23 & 42 & 45 & 68 & 55 & 63 & 96 & 85
\end{array}$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 12

Use a graphing calculator to plot the data and find the quadratic function of best fit.
-A small manufacturing firm collected the following data on advertising expenditures (in thousands of dollars) and total revenue (in thousands of dollars). $$\begin{array} { c | c } 
\text { Advertising, } x & \text { Total Revenue, R } \
\hline 25 & 6430 \
28 & 6432 \
31 & 6434 \
32 & 6434 \
34 & 6434 \
39 & 6431 \
40 & 6432 \
45 & 6420
\end{array}$$ Find the quadratic function of best fit.

Accepted Answer

A)  $R ( x ) = - 0.015 x ^ { 2 } + 4.53 x + 6123$ 
B)  $R ( x ) = - 0.091 x ^ { 2 } + 5.95 x + 6337$ 
C)  $R ( x ) = - 0.024 x ^ { 2 } + 7.13 x + 6209$ 
D)  $R ( x ) = - 0.31 x ^ { 2 } + 2.63 x + 6128$ 
A)  $R ( x ) = - 0.015 x ^ { 2 } + 4.53 x + 6123$ 
B)  $R ( x ) = - 0.091 x ^ { 2 } + 5.95 x + 6337$ 
C)  $R ( x ) = - 0.024 x ^ { 2 } + 7.13 x + 6209$ 
D)  $R ( x ) = - 0.31 x ^ { 2 } + 2.63 x + 6128$

Question 13

Find the zeros of the quadratic function by completing the square. List the x-intercepts of the graph of the function.
-$$f ( x ) = 16 x ^ { 2 } + 56 x + 13$$

Accepted Answer

A)  $x = - \frac { 1 } { 16 } , x = - \frac { 13 } { 16 }$ 
B)  $x = - \frac { 13 } { 8 } , x = \frac { 13 } { 8 }$ 
C)  $x = \frac { 1 } { 4 } , x = \frac { 13 } { 4 }$ 
D)  $x = - \frac { 1 } { 4 } , x = - \frac { 13 } { 4 }$ 
A)  $x = - \frac { 1 } { 16 } , x = - \frac { 13 } { 16 }$ 
B)  $x = - \frac { 13 } { 8 } , x = \frac { 13 } { 8 }$ 
C)  $x = \frac { 1 } { 4 } , x = \frac { 13 } { 4 }$ 
D)  $x = - \frac { 1 } { 4 } , x = - \frac { 13 } { 4 }$

Question 14

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

Accepted Answer

A)  domain: $\{ x \mid x \leq - 2 \}$
 range: $\{ y \mid y \leq 9 \}$ 
B)  domain: all real numbers 
range: $\{ y \mid y \leq - 9 \}$ 
C)  domain: all real numbers
 range: all real numbers 
D)  domain: all real numbers 
range: $\{ y \mid y \leq 9 \}$ 
A)  domain: $\{ x \mid x \leq - 2 \}$
 range: $\{ y \mid y \leq 9 \}$ 
B)  domain: all real numbers 
range: $\{ y \mid y \leq - 9 \}$ 
C)  domain: all real numbers
 range: all real numbers 
D)  domain: all real numbers 
range: $\{ y \mid y \leq 9 \}$

Question 15

Solve the inequality.
-$64 x ^ { 2 } + 9 < 48 x$

Accepted Answer

A)  $\left( - \infty , \frac { 3 } { 8 } \right)$ 
B)  $\left( - \frac { 3 } { 8 } , \infty \right)$ 
C)  No real solution 
D)  $\left( - \infty , - \frac { 3 } { 8 } \right)$ 
A)  $\left( - \infty , \frac { 3 } { 8 } \right)$ 
B)  $\left( - \frac { 3 } { 8 } , \infty \right)$ 
C)  No real solution 
D)  $\left( - \infty , - \frac { 3 } { 8 } \right)$

Question 16

Graph the function f by starting with the graph of y = x2 and using transformations (shifting, compressing, stretching,
and/or reflection).
-$f(x)=-x^{2}+10 x-24$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 17

Use the slope and y-intercept to graph the linear function.
-$G(x)=-3 x$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 18

Solve the equation.
-$$| 14 x | = 2 x ^ { 2 }$$

Accepted Answer

A)  $\{ 0,7 , - 7 \}$ 
B)  $\{ 0 , - 7 \}$ 
C)  $\{ 0,7 \}$ 
D)  No real solutions 
A)  $\{ 0,7 , - 7 \}$ 
B)  $\{ 0 , - 7 \}$ 
C)  $\{ 0,7 \}$ 
D)  No real solutions

Question 19

Solve the problem.
-Suppose that the quantity supplied S and quantity demanded D of baseball caps at a major league game are given by the functions S(p) = 5,000 - 100p and D(p) = 150p, where p is the price. Find the equilibrium price for
Caps at the game. Then find the equilibrium quantity.

Accepted Answer

A)  $20, $3,000 
B)  $33, $1,700 
C)  $50, $0 
D)  $50, $3,000 
A)  $20, $3,000 
B)  $33, $1,700 
C)  $50, $0 
D)  $50, $3,000

Question 20

Graph the function f by starting with the graph of y = x2 and using transformations (shifting, compressing, stretching,
and/or reflection).
-$f(x)=-x^{2}+2 x$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Determine the domain and the range of the function. - $f ( x ) = x ^ { 2 } + 8 x + 7$

Find the vertex and axis of symmetry of the graph of the function. - $f ( x ) = x ^ { 2 } + 2 x - 3$

Find the real zeros of the function. List the x-intercepts of the graph of the function. - $G ( x ) = x ^ { 4 } - 23 x ^ { 2 } - 50$

Solve the problem. -The price $p$ (in dollars) and the quantity $x$ sold of a certain product obey the demand equation $x = - 6 p + 120 , \quad 0 \leq p \leq 20$ . What quantity $x$ maximizes revenue? What is the maximum revenue?

Determine the average rate of change for the function. -h(x) = -4x + 10

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary. - 2 4 6 8 10 15 37 60 75 94

Solve the equation. - $| x | = 7$

Find the real zeros, if any, of each quadratic function using the quadratic formula. List the x-intercepts, if any, of the graph of the function. - $h ( x ) = x ^ { 2 } - 4 x + 20$

Solve the problem. -A lumber yard has fixed costs of $4,726.80 per day and variable costs of $0.1 per board-foot produced. Lumber sells for $1.90 per board-foot. How many board-feet must be produced and sold daily to break even?

Plot a scatter diagram. - 15 21 36 46 58 70 71 84 95 10 23 42 45 68 55 63 96 85 $Plot a scatter diagram. - \begin{array} { l | c c c c c c c c c } \mathrm { x } & 15 & 21 & 36 & 46 & 58 & 70 & 71 & 84 & 95 \\ \hline \mathrm { y } & 10 & 23 & 42 & 45 & 68 & 55 & 63 & 96 & 85 \end{array}$

Find the zeros of the quadratic function by completing the square. List the x-intercepts of the graph of the function. - $f ( x ) = 16 x ^ { 2 } + 56 x + 13$

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

Solve the inequality. - $64 x ^ { 2 } + 9 < 48 x$

Use the slope and y-intercept to graph the linear function. - $G(x)=-3 x$

Solve the equation. - $| 14 x | = 2 x ^ { 2 }$

Solve the problem. -Suppose that the quantity supplied S and quantity demanded D of baseball caps at a major league game are given by the functions S(p) = 5,000 - 100p and D(p) = 150p, where p is the price. Find the equilibrium price for Caps at the game. Then find the equilibrium quantity.

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 2: Linear and Quadratic Functions

Determine the domain and the range of the function. - f(x)=x2+8x+7f ( x ) = x ^ { 2 } + 8 x + 7f(x)=x2+8x+7

Find the vertex and axis of symmetry of the graph of the function. - f(x)=x2+2x−3f ( x ) = x ^ { 2 } + 2 x - 3f(x)=x2+2x−3

Find the real zeros of the function. List the x-intercepts of the graph of the function. - G(x)=x4−23x2−50G ( x ) = x ^ { 4 } - 23 x ^ { 2 } - 50G(x)=x4−23x2−50

Solve the problem. -The price ppp (in dollars) and the quantity xxx sold of a certain product obey the demand equation x=−6p+120,0≤p≤20x = - 6 p + 120 , \quad 0 \leq p \leq 20x=−6p+120,0≤p≤20 . What quantity xxx maximizes revenue? What is the maximum revenue?

Determine the average rate of change for the function. -h(x) = -4x + 10

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary. - 2 4 6 8 10 15 37 60 75 94

Solve the equation. - ∣x∣=7| x | = 7∣x∣=7

Find the real zeros, if any, of each quadratic function using the quadratic formula. List the x-intercepts, if any, of the graph of the function. - h(x)=x2−4x+20h ( x ) = x ^ { 2 } - 4 x + 20h(x)=x2−4x+20

Solve the problem. -A lumber yard has fixed costs of $4,726.80 per day and variable costs of $0.1 per board-foot produced. Lumber sells for $1.90 per board-foot. How many board-feet must be produced and sold daily to break even?

Plot a scatter diagram. - 15 21 36 46 58 70 71 84 95 10 23 42 45 68 55 63 96 85

Find the zeros of the quadratic function by completing the square. List the x-intercepts of the graph of the function. - f(x)=16x2+56x+13f ( x ) = 16 x ^ { 2 } + 56 x + 13f(x)=16x2+56x+13

Determine the domain and the range of the function. - f(x)=−x2+4x+5f ( x ) = - x ^ { 2 } + 4 x + 5f(x)=−x2+4x+5

Solve the inequality. - 64x2+9<48x64 x ^ { 2 } + 9 < 48 x64x2+9<48x

Graph the function f by starting with the graph of y = x2 and using transformations (shifting, compressing, stretching, and/or reflection). - f(x)=−x2+10x−24f(x)=-x^{2}+10 x-24f(x)=−x2+10x−24

Use the slope and y-intercept to graph the linear function. - G(x)=−3xG(x)=-3 xG(x)=−3x

Solve the equation. - ∣14x∣=2x2| 14 x | = 2 x ^ { 2 }∣14x∣=2x2

Solve the problem. -Suppose that the quantity supplied S and quantity demanded D of baseball caps at a major league game are given by the functions S(p) = 5,000 - 100p and D(p) = 150p, where p is the price. Find the equilibrium price for Caps at the game. Then find the equilibrium quantity.

Graph the function f by starting with the graph of y = x2 and using transformations (shifting, compressing, stretching, and/or reflection). - f(x)=−x2+2xf(x)=-x^{2}+2 xf(x)=−x2+2x

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Determine the domain and the range of the function. - $f ( x ) = x ^ { 2 } + 8 x + 7$

Find the vertex and axis of symmetry of the graph of the function. - $f ( x ) = x ^ { 2 } + 2 x - 3$

Find the real zeros of the function. List the x-intercepts of the graph of the function. - $G ( x ) = x ^ { 4 } - 23 x ^ { 2 } - 50$

Solve the problem. -The price $p$ (in dollars) and the quantity $x$ sold of a certain product obey the demand equation $x = - 6 p + 120 , \quad 0 \leq p \leq 20$ . What quantity $x$ maximizes revenue? What is the maximum revenue?

Solve the equation. - $| x | = 7$

Find the real zeros, if any, of each quadratic function using the quadratic formula. List the x-intercepts, if any, of the graph of the function. - $h ( x ) = x ^ { 2 } - 4 x + 20$

Plot a scatter diagram. - 15 21 36 46 58 70 71 84 95 10 23 42 45 68 55 63 96 85 $Plot a scatter diagram. - \begin{array} { l | c c c c c c c c c } \mathrm { x } & 15 & 21 & 36 & 46 & 58 & 70 & 71 & 84 & 95 \\ \hline \mathrm { y } & 10 & 23 & 42 & 45 & 68 & 55 & 63 & 96 & 85 \end{array}$

Find the zeros of the quadratic function by completing the square. List the x-intercepts of the graph of the function. - $f ( x ) = 16 x ^ { 2 } + 56 x + 13$

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

Solve the inequality. - $64 x ^ { 2 } + 9 < 48 x$

Use the slope and y-intercept to graph the linear function. - $G(x)=-3 x$

Solve the equation. - $| 14 x | = 2 x ^ { 2 }$