Question 1

Determine if the vertex of the graph is a maximum point or a minimum point.
-$y = - ( x + 1 ) ^ { 2 }$

Accepted Answer

A)  Minimum 
B)  Maximum 
A)  Minimum 
B)  Maximum

Question 2

Determine if the graph of the function is concave up or concave down
-$y = 4 ( x + 1 ) ^ { 2 } + 2$

Accepted Answer

A)  Concave up 
B)  Concave down 
A)  Concave up 
B)  Concave down

Question 3

Does it appear that a linear model or a power model is the best fit for the data given in the table below? Explain
your choice. $$\begin{array} { c | c } 
x & y \
\hline 2 & 8 \
\hline 4 & 16 \
\hline 6 & 28 \
\hline 8 & 36
\end{array}$$

Accepted Answer

Since the first differences ar

Question 4

If a ball is thrown upward at 64 feet per second from the top of a building that is 110 feet high, the height of the ball can be modeled by $S = 110 + 64 t - 16 t ^ { 2 }$ feet, where t is the number of seconds after the ball is thrown. What
Is the ball's maximum height?

Accepted Answer

A)  302 ft 
B)  110 ft 
C)  158 ft 
D)  174 ft 
A)  302 ft 
B)  110 ft 
C)  158 ft 
D)  174 ft

Question 5

Use factoring to solve the equation
-$$3 x ^ { 2 } - 23 x = 8$$

Accepted Answer

A)  $- \frac { 1 } { 3 } , 8$ 
B)  $- 3,8$ 
C) $ - \frac { 1 } { 8 } , - 3$ 
D)  $- \frac { 1 } { 8 } , 3$ 
A)  $- \frac { 1 } { 3 } , 8$ 
B)  $- 3,8$ 
C) $ - \frac { 1 } { 8 } , - 3$ 
D)  $- \frac { 1 } { 8 } , 3$

Question 6

Use a graphing utility as an aid in factoring to
-$$2 s ^ { 2 } - 136 s = - 1800$$

Accepted Answer

A)  $\mathrm { s } = 50 , \mathrm {~s} = - 18$ 
B)  $\mathrm { s } = 5 , \mathrm {~s} = 180$ 
C)  $\mathrm { s } = 50 , \mathrm {~s} = 18$ 
D)  $\mathrm { s } = 37 , \mathrm {~s} = 20$ 
A)  $\mathrm { s } = 50 , \mathrm {~s} = - 18$ 
B)  $\mathrm { s } = 5 , \mathrm {~s} = 180$ 
C)  $\mathrm { s } = 50 , \mathrm {~s} = 18$ 
D)  $\mathrm { s } = 37 , \mathrm {~s} = 20$

Question 7

Graph
-$$y = 1 - \frac { 1 } { x }$$

Accepted Answer

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

Question 8

The charges for renting a moving van are $\$ 65$ for the first 40 miles and $\$ 7$ for each additional mile. Assume that a fraction of a mile is rounded up.
a. Determine the cost of driving the van 98 miles.
b. Find a symbolic representation for a function $\mathrm { f }$ that computes the cost of driving the van $x$ miles, where $0 < x \leq$ (Hint: express f as a piecewise-constant function.)

Accepted Answer

A)  a. $\$ 6776$; 
b. $f ( x ) = \left\{ \begin{array} { l l } 65 & \text { if } 0 < x \leq 40 \ 65 x + 7 ( x - 40 ) & \text { if } 40 < x \leq 100 \end{array} \right.$ 
B)  a. $\$ 471 ;$ 
b.$f ( x ) = \left\{ \begin{array} { l l } 65 & \text { if } 0 < x \leq 40 \ 65 + 7 ( x - 40 ) & \text { if } 40 < x \leq 100 \end{array} \right.$ 
C)  a. $\$ 471 ;$
 b. $f ( x ) = \left\{ \begin{array} { l l } 65 & \text { if } 0 < x \leq 40 \ 65 + 7 ( x + 40 ) & \text { if } 40 < x \leq 100 \end{array} \right.$ 
D)  a. $\$ 1031$; 
b. $f ( x ) = \left\{ \begin{array} { l l } 65 & \text { if } 0 < x \leq 40 \ 65 + 7 ( x + 40 ) & \text { if } 40 < x \leq 100 \end{array} \right.$ 
A)  a. $\$ 6776$; 
b. $f ( x ) = \left\{ \begin{array} { l l } 65 & \text { if } 0 < x \leq 40 \ 65 x + 7 ( x - 40 ) & \text { if } 40 < x \leq 100 \end{array} \right.$ 
B)  a. $\$ 471 ;$ 
b.$f ( x ) = \left\{ \begin{array} { l l } 65 & \text { if } 0 < x \leq 40 \ 65 + 7 ( x - 40 ) & \text { if } 40 < x \leq 100 \end{array} \right.$ 
C)  a. $\$ 471 ;$
 b. $f ( x ) = \left\{ \begin{array} { l l } 65 & \text { if } 0 < x \leq 40 \ 65 + 7 ( x + 40 ) & \text { if } 40 < x \leq 100 \end{array} \right.$ 
D)  a. $\$ 1031$; 
b. $f ( x ) = \left\{ \begin{array} { l l } 65 & \text { if } 0 < x \leq 40 \ 65 + 7 ( x + 40 ) & \text { if } 40 < x \leq 100 \end{array} \right.$

Question 9

Graph the function.
-$$f ( x ) = \left\{ \begin{array} { l l } 
| x | + 2 , & \text { if } x < 0 \
2 , & \text { if } x \geq 0
\end{array} \right.$$

Accepted Answer

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

Question 10

Find a power function that models the data in the table. Round to three decimal places if necessary.
-The table shows the number of new cases of a certain disease among women in six consecutive years. Data are in thousands rounded to the nearest hundred. $\begin{array} { l c } \frac { \text { Year } } { 2005 } & \text { New Cases (thousands) } \ & 3.0 \ 2007 & 3.4 \ 2008 & 4.6 \ 2009 & 5.4 \ 2010 & 6.0 \ & 16.1 \end{array}$
Let $x = 1$ correspond to 2005 and let $y$ be the number of new cases (in thousands) among women in year $x$. Find a quadratic function to model the data. Use the unrounded function to determine in what year the number of new cases among women will reach 20,000 .

Accepted Answer

A)  1992 
B)  1993 
C)  1994 
D)  1995 
A)  1992 
B)  1993 
C)  1994 
D)  1995

Question 11

The cost $C$ of producing $t$ units is given by $C ( t ) = 3 t ^ { 2 } + 8 t$, and the revenue $R$ generated from selling $t$ units is given by $R ( t ) = 4 t ^ { 2 } + t$. For what values of $t$ will there be a profit?

Accepted Answer

A)  There will be a profit when more than 8 units are sold 
B)  There will be a profit when more than 9 units are sold. 
C)  There will be a profit when more than 7 units are sold. 
D)  There will be a profit when 0 units are sold. 
A)  There will be a profit when more than 8 units are sold 
B)  There will be a profit when more than 9 units are sold. 
C)  There will be a profit when more than 7 units are sold. 
D)  There will be a profit when 0 units are sold.

Question 12

Use a graphing utility to find or approximate the x-intercepts of the graph of the quadratic function.
-$$y = 9 k ^ { 2 } - 62 k - 7$$

Accepted Answer

A)  $\left( \frac { 1 } { 62 } , 0 \right) , \left( - \frac { 1 } { 9 } , 0 \right)$ 
B)  $\left( - \frac { 1 } { 9 } , 0 \right)$, 
C)  $\left( - \frac { 1 } { 9 } , 0 \right) , ( 7,0 )$ 
D)  $( - 9,0 ) , ( 7,0 )$ 
A)  $\left( \frac { 1 } { 62 } , 0 \right) , \left( - \frac { 1 } { 9 } , 0 \right)$ 
B)  $\left( - \frac { 1 } { 9 } , 0 \right)$, 
C)  $\left( - \frac { 1 } { 9 } , 0 \right) , ( 7,0 )$ 
D)  $( - 9,0 ) , ( 7,0 )$

Question 13

Determine if the graph of the function is concave up or concave down
-$y = - ( x + 5 ) ^ { 2 } - 3$

Accepted Answer

A)  Concave up 
B)  Concave down 
A)  Concave up 
B)  Concave down

Question 14

Solve the equation.
-$$| 5 m + 3 | + 5 = 10$$

Accepted Answer

A)  $\frac { 2 } { 5 } , - \frac { 8 } { 5 }$ 
B)  $\frac { 2 } { 5 }$ 
C)  $\frac { 2 } { 3 } , - \frac { 8 } { 3 }$ 
D)  $- \frac { 2 } { 5 } , \frac { 8 } { 5 }$ 
A)  $\frac { 2 } { 5 } , - \frac { 8 } { 5 }$ 
B)  $\frac { 2 } { 5 }$ 
C)  $\frac { 2 } { 3 } , - \frac { 8 } { 3 }$ 
D)  $- \frac { 2 } { 5 } , \frac { 8 } { 5 }$

Question 15

Determine if the vertex of the graph is a maximum point or a minimum point.
-$f ( x ) = - 2 x ^ { 2 } - 2 x + 2$

Accepted Answer

A)  Maximum 
B)  Minimum 
A)  Maximum 
B)  Minimum

Question 16

If money is invested for 3 years with interest compounded annually, the future value of the investment varies directly as the cube of $1 + r$ r, where r is the interest rate. If the future value of the investment is $9317.00 when the
Rate is 10%, what rate gives a future value of $8575.30? Round to the nearest whole percent.

Accepted Answer

A)  6% 
B)  8% 
C)  7% 
D)  9% 
A)  6% 
B)  8% 
C)  7% 
D)  9%

Question 17

Use the square root method to
-$$7 \mathrm { z } ^ { 2 } + 2 = 849$$

Accepted Answer

A)  $\pm 12$ 
B)  $424.5$ 
C)  $\pm 11$ 
D)  11 
A)  $\pm 12$ 
B)  $424.5$ 
C)  $\pm 11$ 
D)  11

Question 18

Use the quadratic formula to
-$$x ^ { 2 } + 9 x - 22 = 0$$

Accepted Answer

A)  11,2 
B)  $- 11,2$ 
C)  $- 11,1$ 
D)  $11 , - 2$ 
A)  11,2 
B)  $- 11,2$ 
C)  $- 11,1$ 
D)  $11 , - 2$

Question 19

Solve the equation by completing the square.
-$$\mathrm { t } ^ { 2 } - \mathrm { t } - 9 = 0$$

Accepted Answer

A)  $\frac { 1 \pm i \sqrt { 35 } } { 2 }$ 
B)  $\frac { - 1 \pm \sqrt { 37 } } { 2 }$ 
C)  $\frac { 1 \pm \sqrt { 37 } } { 2 }$ 
D)  $1 \pm \sqrt { 37 }$ 
A)  $\frac { 1 \pm i \sqrt { 35 } } { 2 }$ 
B)  $\frac { - 1 \pm \sqrt { 37 } } { 2 }$ 
C)  $\frac { 1 \pm \sqrt { 37 } } { 2 }$ 
D)  $1 \pm \sqrt { 37 }$

Question 20

Find a power function that models the data in the table. Round to three decimal places if necessary.
-The percent of people who say they plan to stay in the same job position until they retire has decreased over recent years, as shown in the table below. $\begin{array}{c|cccccc}
\text { Year } & 2005 & 2006 & 2007 & 2008 & 2009 & 2010 \
\hline \text { Percent } & 42 & 38 & 35 & 34 & 30 & 26
\end{array}$

Find a power function that models the data in the table using an input equal to the number of years from 2000. R values to the nearest thousandth.

Accepted Answer

A)  $y = - 0.638 x ^ { 120.077 }$ 
B)  $y = 120.077 x ^ { - 0.638 }$ 
C)  $y = 43.934 x ^ { - 0.240 }$ 
D)  $y = 52.857 x ^ { - 0.071 }$ 
A)  $y = - 0.638 x ^ { 120.077 }$ 
B)  $y = 120.077 x ^ { - 0.638 }$ 
C)  $y = 43.934 x ^ { - 0.240 }$ 
D)  $y = 52.857 x ^ { - 0.071 }$

Determine if the vertex of the graph is a maximum point or a minimum point. - $y = - ( x + 1 ) ^ { 2 }$

Determine if the graph of the function is concave up or concave down - $y = 4 ( x + 1 ) ^ { 2 } + 2$

Does it appear that a linear model or a power model is the best fit for the data given in the table below? Explain your choice. x y 2 8 4 16 6 28 8 36

If a ball is thrown upward at 64 feet per second from the top of a building that is 110 feet high, the height of the ball can be modeled by $S = 110 + 64 t - 16 t ^ { 2 }$ feet, where t is the number of seconds after the ball is thrown. What Is the ball's maximum height?

Use factoring to solve the equation - $3 x ^ { 2 } - 23 x = 8$

Use a graphing utility as an aid in factoring to - $2 s ^ { 2 } - 136 s = - 1800$

Graph - $y = 1 - \frac { 1 } { x }$ $Graph - y = 1 - \frac { 1 } { x }$

Graph the function. - $f ( x ) = \left\{ \begin{array} { l l } | x | + 2 , & \text { if } x < 0 \\2 , & \text { if } x \geq 0\end{array} \right.$ $Graph the function. - f ( x ) = \left\{ \begin{array} { l l } | x | + 2 , & \text { if } x < 0 \\ 2 , & \text { if } x \geq 0 \end{array} \right.$

The cost $C$ of producing $t$ units is given by $C ( t ) = 3 t ^ { 2 } + 8 t$ , and the revenue $R$ generated from selling $t$ units is given by $R ( t ) = 4 t ^ { 2 } + t$ . For what values of $t$ will there be a profit?

Use a graphing utility to find or approximate the x-intercepts of the graph of the quadratic function. - $y = 9 k ^ { 2 } - 62 k - 7$

Determine if the graph of the function is concave up or concave down - $y = - ( x + 5 ) ^ { 2 } - 3$

Solve the equation. - $| 5 m + 3 | + 5 = 10$

Determine if the vertex of the graph is a maximum point or a minimum point. - $f ( x ) = - 2 x ^ { 2 } - 2 x + 2$

Use the square root method to - $7 \mathrm { z } ^ { 2 } + 2 = 849$

Use the quadratic formula to - $x ^ { 2 } + 9 x - 22 = 0$

Solve the equation by completing the square. - $\mathrm { t } ^ { 2 } - \mathrm { t } - 9 = 0$

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

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Higher-Degree Polynomial and Rational Functions

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Exam 3: Quadratic, Piecewise-Defined, and Power Functions

Determine if the vertex of the graph is a maximum point or a minimum point. - y=−(x+1)2y = - ( x + 1 ) ^ { 2 }y=−(x+1)2

Determine if the graph of the function is concave up or concave down - y=4(x+1)2+2y = 4 ( x + 1 ) ^ { 2 } + 2y=4(x+1)2+2

Does it appear that a linear model or a power model is the best fit for the data given in the table below? Explain your choice. x y 2 8 4 16 6 28 8 36

Use factoring to solve the equation - 3x2−23x=83 x ^ { 2 } - 23 x = 83x2−23x=8

Use a graphing utility as an aid in factoring to - 2s2−136s=−18002 s ^ { 2 } - 136 s = - 18002s2−136s=−1800

Graph - y=1−1xy = 1 - \frac { 1 } { x }y=1−x1​

Graph the function. - f(x)={∣x∣+2, if x<02, if x≥0f ( x ) = \left\{ \begin{array} { l l } | x | + 2 , & \text { if } x < 0 \\2 , & \text { if } x \geq 0\end{array} \right.f(x)={∣x∣+2,2,​ if x<0 if x≥0​

The cost CCC of producing ttt units is given by C(t)=3t2+8tC ( t ) = 3 t ^ { 2 } + 8 tC(t)=3t2+8t , and the revenue RRR generated from selling ttt units is given by R(t)=4t2+tR ( t ) = 4 t ^ { 2 } + tR(t)=4t2+t . For what values of ttt will there be a profit?

Use a graphing utility to find or approximate the x-intercepts of the graph of the quadratic function. - y=9k2−62k−7y = 9 k ^ { 2 } - 62 k - 7y=9k2−62k−7

Determine if the graph of the function is concave up or concave down - y=−(x+5)2−3y = - ( x + 5 ) ^ { 2 } - 3y=−(x+5)2−3

Solve the equation. - ∣5m+3∣+5=10| 5 m + 3 | + 5 = 10∣5m+3∣+5=10

Determine if the vertex of the graph is a maximum point or a minimum point. - f(x)=−2x2−2x+2f ( x ) = - 2 x ^ { 2 } - 2 x + 2f(x)=−2x2−2x+2

Use the square root method to - 7z2+2=8497 \mathrm { z } ^ { 2 } + 2 = 8497z2+2=849

Use the quadratic formula to - x2+9x−22=0x ^ { 2 } + 9 x - 22 = 0x2+9x−22=0

Solve the equation by completing the square. - t2−t−9=0\mathrm { t } ^ { 2 } - \mathrm { t } - 9 = 0t2−t−9=0