Question 1

Graph the parabola and the axis of symmetry. Label the coordinates of the vertex, and write the
equation of the axis of symmetry.
-$$y = - ( x - 5 ) ^ { 2 } + 2$$

Accepted Answer

A)

Vertex $( - 5 , - 2 )$
axis of symmetry: $x = - 5$ 
B) 
Vertex $( - 5,2 )$
axis of symmetry: $x = - 5$ 
C)

Vertex $( 5 , - 2 )$
axis of symmetry: $x = 5$ 
D)

Vertex $( 5,2 )$
axis of symmetry: $x = 5$

Question 2

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The amount of a person's paycheck varies as the number of hours worked.

Accepted Answer

The answer of Write the word or phrase that best...

Question 3

a. Identify the horizontal asymptote (if any).
b. If the graph of the function has a horizontal asymptote, determine the point where the graph crosses the
horizontal asymptote.
-$$f ( x ) = \frac { x ^ { 2 } - 7 x ^ { 2 } + 1 } { 8 x + 7 }$$

Accepted Answer

A)  a. $y = \frac { 1 } { 8 }$
b. $\left( \frac { 1 } { 7 } , \frac { 1 } { 8 } \right)$ 
B)  a. $y = 0$
b. $\left( \frac { 1 } { 7 } , 0 \right)$ 
C)  a. $y = 1$
b. $\left( \frac { 1 } { 7 } , 1 \right)$ 
D)  a. No horizontal asymptote
b. Not applicable

Question 4

Solve the problem.
-The area of a picture projected on a wall varies directly as the square of the distance from the projector to the wall.
a. If a $12 - \mathrm { ft }$ distance produces a $81 \mathrm { ft } ^ { 2 }$ picture, what is the area of the picture when the projection unit is moved to a distance of $16 \mathrm { ft }$ from the wall?
b. If the projected image is $324 \mathrm { ft } ^ { 2 }$, how far is the projector from the wall?

Accepted Answer

A)  a. $108 \mathrm { ft } ^ { 2 }$;
b. $48 \mathrm { ft }$ 
B)  a. $196 \mathrm { ft } ^ { 2 }$;
b. $54 \mathrm { ft }$ 
C)  a. $169 \mathrm { ft } ^ { 2 }$;
b. $36 \mathrm { ft }$ 
D)  a. $144 \mathrm { ft } ^ { 2 }$;
b. $24 \mathrm { ft }$

Question 5

Determine the x- and y-intercepts for the given function.
-$$f ( x ) = - ( x - 2 ) ^ { 2 } - 4$$

Accepted Answer

A)  $x$-intercepts: $( 0,0 )$ and $( 4,0 )$
$y$-intercept: $( 0 , - 8 )$ 
B)  $x$-intercept: $( 2,0 )$
$y$-intercept: $( 0 , - 4 )$ 
C)  $x$-intercept: none
$y$-intercept: $( 0 , - 8 )$ 
D)  $x$-intercept: $( 2,0 )$
$y$-intercept: $( 0,4 )$

Question 6

Find the constant of variation k.
-$N$ varies jointly as $t$ and $p$. When $t$ is 6 and $p$ is $3 , N$ is 36 .

Accepted Answer

A)  $k = 72$ 
B)  $k = 648$ 
C)  $k = 2$ 
D)  $k = 18$

Question 7

Find the value of b that gives the function the given maximum value.
-$f ( x ) = - x ^ { 2 } + b x + 2 ;$ maximum value 6

Accepted Answer

A)  $b = - 2$ or $b = 2$ 
B)  $b = - 4$ or $b = 4$ 
C)  $b = 4$ 
D)  $b = 2$

Question 8

Choose the one alternative that best completes the statement or answers the question.
The graph of y = f (x) is given. Solve the inequality.
-$$f ( x ) < 0$$

Accepted Answer

A)  $[ 1,2 ]$ 
B)  $( 1,2 )$ 
C)  $( - \infty , 1 ) \cup ( 2 , \infty )$ 
D)  $( - \infty , 1 ] \cup [ 2 , \infty )$

Question 9

Graph the function by using transformations of the graph of $y = \frac { 1 } { x ^ { 2 } }$
-$$m ( x ) = \frac { 1 } { x ^ { 2 } } + 1$$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 10

Solve the problem.
-The monthly profit for a small company that makes long-sleeve T-shirts depends on the price per shirt. If the price is too high, sales will drop. If the price is too low, the revenue brought in may not
Cover the cost to produce the shirts. After months of data collection, the sales team determines that
The monthly profit is approximated by $f ( p ) = - 33 p ^ { 2 } + 1,254 p - 10,763$ , where p is the price per shirt
And f p is the monthly profit based on that price. Find the price that generates the maximum profit
And find the maximum profit.

Accepted Answer

A)  $p = \$ 19$
$f ( p ) = \$ 1,150$ 
B)  $p = \$ 38$
$f ( p ) = \$ 10,763$ 
C)  $p = \$ 19$
$f ( p ) = \$ 24,976$ 
D)  $p = \$ 38$
$f ( p ) = \$ 1,150$

Question 11

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The of a polynomial f (x) are the solutions (or roots) of the equation f (x) = 0.

Accepted Answer

The answer of Write the word or phrase that best...

Question 12

a. Identify the horizontal asymptote (if any).
b. If the graph of the function has a horizontal asymptote, determine the point where the graph crosses the
horizontal asymptote.
-$$s ( x ) = \frac { 5 x - 10 } { x ^ { 2 } + 5 x - 4 }$$

Accepted Answer

A)  a. $y = 0$
b. $\left( - \frac { 5 } { 2 } , 0 \right)$ 
B)  a. $y = 2$
b. $( 0,2 )$ 
C)  a. $y = 0$
b. $( 2,0 )$ 
D)  a. No horizontal asymptote
b. Not applicable

Question 13

Choose the one alternative that best completes the statement or answers the question.
Determine the end behavior of the graph of the function.
-$$f ( x ) = 8 x ^ { 6 } + 3 x ^ { 5 } + 3 x ^ { 4 } + 7$$

Accepted Answer

A)  Up left and down right 
B)  Down left and down right 
C)  Down left and up right 
D)  Up left and up right

Question 14

Solve the problem.
-The strength of a wooden beam varies jointly as the width of the beam and the square of the thickness of the beam, and inversely as the length of the beam. A beam that is 48 in. long, 6 in. wide, and 4 in. thick can support a load of $1,668 \mathrm { lb }$. Find the maximum load that can be safely supported by a board that is $8 \mathrm { in }$. wide, $120 \mathrm { in }$. long, and 5 in. thick.

Accepted Answer

A)  $1,529 \mathrm { lb }$ 
B)  $1,676 \mathrm { lb }$ 
C)  $1,390 \mathrm { lb }$ 
D)  $1,533 \mathrm { lb }$

Question 15

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-A student's grade on a test varies as the number of hours the student spends studying for the test.

Accepted Answer

The answer of Write the word or phrase that best...

Question 16

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-If $\sqrt { 5 }$ is a zero of a polynomial, then ( $( x - \sqrt { 5 } )$ ) is a factor of the polynomial.

Accepted Answer

A) True 
 B)False

Question 17

Write a polynomial f (x) that meets the given conditions.
-Polynomial of lowest degree with zeros of $- 2$ (multiplicity 2 ) and 3 (multiplicity 2 ) and with $f ( 0 ) = - 108$

Accepted Answer

A)  $f ( x ) = - 3 x ^ { 4 } + 6 x ^ { 3 } + 33 x ^ { 2 } - 36 x - 108$ 
B)  $f ( x ) = - 3 x ^ { 4 } + 6 x ^ { 3 } - 111 x ^ { 2 } - 36 x - 108$ 
C)  $f ( x ) = - 3 x ^ { 4 } + 6 x ^ { 3 } + 33 x ^ { 2 } - 18 x - 108$ 
D)  $f ( x ) = x ^ { 4 } - 2 x ^ { 3 } - 11 x ^ { 2 } + 12 x - 108$

Question 18

Identify the asymptotes.
-$$f ( x ) = \frac { 2 x ^ { 2 } + 7 } { x }$$

Accepted Answer

A)  Vertical asymptote: $x = 2$; 
B)  Vertical asymptote: $x = 0$;
Slant asymptote: $y = 2 x + 7$ 
C)  Vertical asymptote: $x = 0$; 
D)  Vertical asymptote: $x = 0$;
Slant asymptote: $y = 2 x$

Question 19

Solve the problem.
-An automobile manufacturer can produce up to 300 cars per day. The profit made from the sale of these vehicles can be modeled by the function $P ( x ) = - 10 x ^ { 2 } + 1,900 x - 34,000$ where P(x) is the
Profit in dollars and x is the number of automobiles made and sold. How many cars should be made
And sold to maximize profit?

Accepted Answer

A)  1,900 
B)  95 
C)  45 
D)  190

Question 20

Solve the problem.
-Use synthetic division and the remainder theorem to determine if $$[ x - ( 3 - 2 i ) ]$$ is a factor of $$f ( x ) = x ^ { 2 } - 6 x + 13$$

Accepted Answer

A)  No 
B)  Yes

Exam 3: Polynomial and Rational Functions

Graph the parabola and the axis of symmetry. Label the coordinates of the vertex, and write the equation of the axis of symmetry. - $y = - ( x - 5 ) ^ { 2 } + 2$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The amount of a person's paycheck varies as the number of hours worked.

a. Identify the horizontal asymptote (if any) . b. If the graph of the function has a horizontal asymptote, determine the point where the graph crosses the horizontal asymptote. - $f ( x ) = \frac { x ^ { 2 } - 7 x ^ { 2 } + 1 } { 8 x + 7 }$

Determine the x- and y-intercepts for the given function. - $f ( x ) = - ( x - 2 ) ^ { 2 } - 4$

Find the constant of variation k. - $N$ varies jointly as $t$ and $p$ . When $t$ is 6 and $p$ is $3 , N$ is 36 .

Find the value of b that gives the function the given maximum value. - $f ( x ) = - x ^ { 2 } + b x + 2 ;$ maximum value 6

Graph the function by using transformations of the graph of $y = \frac { 1 } { x ^ { 2 } }$ - $m ( x ) = \frac { 1 } { x ^ { 2 } } + 1$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The of a polynomial f (x) are the solutions (or roots) of the equation f (x) = 0.

a. Identify the horizontal asymptote (if any) . b. If the graph of the function has a horizontal asymptote, determine the point where the graph crosses the horizontal asymptote. - $s ( x ) = \frac { 5 x - 10 } { x ^ { 2 } + 5 x - 4 }$

Choose the one alternative that best completes the statement or answers the question. Determine the end behavior of the graph of the function. - $f ( x ) = 8 x ^ { 6 } + 3 x ^ { 5 } + 3 x ^ { 4 } + 7$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A student's grade on a test varies as the number of hours the student spends studying for the test.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If $\sqrt { 5 }$ is a zero of a polynomial, then ( $( x - \sqrt { 5 } )$ ) is a factor of the polynomial.

Write a polynomial f (x) that meets the given conditions. -Polynomial of lowest degree with zeros of $- 2$ (multiplicity 2 ) and 3 (multiplicity 2 ) and with $f ( 0 ) = - 108$

Identify the asymptotes. - $f ( x ) = \frac { 2 x ^ { 2 } + 7 } { x }$

Solve the problem. -Use synthetic division and the remainder theorem to determine if $[ x - ( 3 - 2 i ) ]$ is a factor of $f ( x ) = x ^ { 2 } - 6 x + 13$

Exam 3: Polynomial and Rational Functions

Graph the parabola and the axis of symmetry. Label the coordinates of the vertex, and write the equation of the axis of symmetry. - y=−(x−5) 2+2y = - ( x - 5 ) ^ { 2 } + 2y=−(x−5) 2+2

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The amount of a person's paycheck varies as the number of hours worked.

a. Identify the horizontal asymptote (if any) . b. If the graph of the function has a horizontal asymptote, determine the point where the graph crosses the horizontal asymptote. - f(x) =x2−7x2+18x+7f ( x ) = \frac { x ^ { 2 } - 7 x ^ { 2 } + 1 } { 8 x + 7 }f(x) =8x+7x2−7x2+1​

Determine the x- and y-intercepts for the given function. - f(x) =−(x−2) 2−4f ( x ) = - ( x - 2 ) ^ { 2 } - 4f(x) =−(x−2) 2−4

Find the constant of variation k. - NNN varies jointly as ttt and ppp . When ttt is 6 and ppp is 3,N3 , N3,N is 36 .

Find the value of b that gives the function the given maximum value. - f(x) =−x2+bx+2;f ( x ) = - x ^ { 2 } + b x + 2 ;f(x) =−x2+bx+2; maximum value 6

Choose the one alternative that best completes the statement or answers the question. The graph of y = f (x) is given. Solve the inequality. - f(x) <0f ( x ) < 0f(x) <0

Graph the function by using transformations of the graph of y=1x2y = \frac { 1 } { x ^ { 2 } }y=x21​ - m(x) =1x2+1m ( x ) = \frac { 1 } { x ^ { 2 } } + 1m(x) =x21​+1

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The of a polynomial f (x) are the solutions (or roots) of the equation f (x) = 0.

a. Identify the horizontal asymptote (if any) . b. If the graph of the function has a horizontal asymptote, determine the point where the graph crosses the horizontal asymptote. - s(x) =5x−10x2+5x−4s ( x ) = \frac { 5 x - 10 } { x ^ { 2 } + 5 x - 4 }s(x) =x2+5x−45x−10​

Choose the one alternative that best completes the statement or answers the question. Determine the end behavior of the graph of the function. - f(x) =8x6+3x5+3x4+7f ( x ) = 8 x ^ { 6 } + 3 x ^ { 5 } + 3 x ^ { 4 } + 7f(x) =8x6+3x5+3x4+7

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A student's grade on a test varies as the number of hours the student spends studying for the test.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If 5\sqrt { 5 }5​ is a zero of a polynomial, then ( (x−5)( x - \sqrt { 5 } )(x−5​) ) is a factor of the polynomial.

Write a polynomial f (x) that meets the given conditions. -Polynomial of lowest degree with zeros of −2- 2−2 (multiplicity 2 ) and 3 (multiplicity 2 ) and with f(0) =−108f ( 0 ) = - 108f(0) =−108

Identify the asymptotes. - f(x) =2x2+7xf ( x ) = \frac { 2 x ^ { 2 } + 7 } { x }f(x) =x2x2+7​

Solve the problem. -Use synthetic division and the remainder theorem to determine if [x−(3−2i) ][ x - ( 3 - 2 i ) ][x−(3−2i) ] is a factor of f(x) =x2−6x+13f ( x ) = x ^ { 2 } - 6 x + 13f(x) =x2−6x+13

Graph the parabola and the axis of symmetry. Label the coordinates of the vertex, and write the equation of the axis of symmetry. - $y = - ( x - 5 ) ^ { 2 } + 2$

a. Identify the horizontal asymptote (if any) . b. If the graph of the function has a horizontal asymptote, determine the point where the graph crosses the horizontal asymptote. - $f ( x ) = \frac { x ^ { 2 } - 7 x ^ { 2 } + 1 } { 8 x + 7 }$

Determine the x- and y-intercepts for the given function. - $f ( x ) = - ( x - 2 ) ^ { 2 } - 4$

Find the constant of variation k. - $N$ varies jointly as $t$ and $p$ . When $t$ is 6 and $p$ is $3 , N$ is 36 .

Find the value of b that gives the function the given maximum value. - $f ( x ) = - x ^ { 2 } + b x + 2 ;$ maximum value 6

Graph the function by using transformations of the graph of $y = \frac { 1 } { x ^ { 2 } }$ - $m ( x ) = \frac { 1 } { x ^ { 2 } } + 1$

a. Identify the horizontal asymptote (if any) . b. If the graph of the function has a horizontal asymptote, determine the point where the graph crosses the horizontal asymptote. - $s ( x ) = \frac { 5 x - 10 } { x ^ { 2 } + 5 x - 4 }$

Choose the one alternative that best completes the statement or answers the question. Determine the end behavior of the graph of the function. - $f ( x ) = 8 x ^ { 6 } + 3 x ^ { 5 } + 3 x ^ { 4 } + 7$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If $\sqrt { 5 }$ is a zero of a polynomial, then ( $( x - \sqrt { 5 } )$ ) is a factor of the polynomial.

Write a polynomial f (x) that meets the given conditions. -Polynomial of lowest degree with zeros of $- 2$ (multiplicity 2 ) and 3 (multiplicity 2 ) and with $f ( 0 ) = - 108$

Identify the asymptotes. - $f ( x ) = \frac { 2 x ^ { 2 } + 7 } { x }$

Solve the problem. -Use synthetic division and the remainder theorem to determine if $[ x - ( 3 - 2 i ) ]$ is a factor of $f ( x ) = x ^ { 2 } - 6 x + 13$