Question 1

Determine which of the rational functions given below has the following feature(s) .
-The x-intercept is (2, 0)

Accepted Answer

A)    f(x) =x+9x−2f ( x )  = \frac { x + 9 } { x - 2 }f(x) =x−2x+9​ 
B)    f(x) =2x−1x+9f ( x )  = \frac { 2 x - 1 } { x + 9 }f(x) =x+92x−1​ 
C)    f(x) =x−2x+9f ( x )  = \frac { x - 2 } { x + 9 }f(x) =x+9x−2​ 
D)    f(x) =x+2x+9f ( x )  = \frac { x + 2 } { x + 9 }f(x) =x+9x+2​

Question 2

Find a polynomial of least degree with only real coefficients and having the given zeros.
- 1−3,1+31 - \sqrt { 3 } , 1 + \sqrt { 3 }1−3​,1+3​ , and  1+i1 + i1+i

Accepted Answer

A)    f(x) =x4+3x3+4x2−1f ( x )  = x ^ { 4 } + 3 x ^ { 3 } + 4 x ^ { 2 } - 1f(x) =x4+3x3+4x2−1 
B)    f(x) =x4−6x3+8x2−4f ( x )  = x ^ { 4 } - 6 x ^ { 3 } + 8 x ^ { 2 } - 4f(x) =x4−6x3+8x2−4 
C)    f(x) =x4−4x3+4x2−4f ( x )  = x ^ { 4 } - 4 x ^ { 3 } + 4 x ^ { 2 } - 4f(x) =x4−4x3+4x2−4 
D)    f(x) =x4+6x3+4x2−4f ( x )  = x ^ { 4 } + 6 x ^ { 3 } + 4 x ^ { 2 } - 4f(x) =x4+6x3+4x2−4

Question 3

Given the equation or other information for a parabola, find the matching description or graph.
-  0 ; b ^ { 2 } - 4 a c > 0\end{array}">f(x) =ax2+bx+ca>0;b2−4ac>0\begin{array} { l } f ( x )  = a x ^ { 2 } + b x + c \a > 0 ; b ^ { 2 } - 4 a c > 0\end{array}f(x) =ax2+bx+ca>0;b2−4ac>0​

Accepted Answer

A)   0 ; b ^ { 2 } - 4 a c > 0 \end{array}  
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Question 4

Sketch the graph of the polynomial function.
- f(x) =13(x+2) 4+3f ( x )  = \frac { 1 } { 3 } ( x + 2 )  ^ { 4 } + 3f(x) =31​(x+2) 4+3

Accepted Answer

A)  
B)  
C)  
D)

Question 5

Determine whether the statement is true or false.
-$$\text { The function } f ( x ) = \frac { 1 } { x } \text { is decreasing on the interval } ( 0 , \infty )$$

Accepted Answer

A) True 
 B)False

Question 6

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
-Zeros of  −3,−1,4- 3 , - 1,4−3,−1,4  and  P(2) =5P ( 2 )  = 5P(2) =5

Accepted Answer

A)    P(x) =x36+19x6−2P ( x )  = \frac { x ^ { 3 } } { 6 } + \frac { 19 x } { 6 } - 2P(x) =6x3​+619x​−2 
B)    P(x) =x36−13x6−2P ( x )  = \frac { x ^ { 3 } } { 6 } - \frac { 13 x } { 6 } - 2P(x) =6x3​−613x​−2 
C)    P(x) =−x36−19x6−2P ( x )  = - \frac { x ^ { 3 } } { 6 } - \frac { 19 x } { 6 } - 2P(x) =−6x3​−619x​−2 
D)    P(x) =−x36+13x6+2P ( x )  = - \frac { x ^ { 3 } } { 6 } + \frac { 13 x } { 6 } + 2P(x) =−6x3​+613x​+2

Question 7

Give all possible rational zeros for the following polynomial.
- P(x) =2x3−5x2+7x−17P ( x )  = 2 x ^ { 3 } - 5 x ^ { 2 } + 7 x - 17P(x) =2x3−5x2+7x−17

Accepted Answer

A)    ±1,±2,±17\pm 1 , \pm 2 , \pm 17±1,±2,±17 
B)    ±1,±2,±17,±172\pm 1 , \pm 2 , \pm 17 , \pm \frac { 17 } { 2 }±1,±2,±17,±217​ 
C)    ±1,±17,±12,±172\pm 1 , \pm 17 , \pm \frac { 1 } { 2 } , \pm \frac { 17 } { 2 }±1,±17,±21​,±217​ 
D)    ±1,±117,±2,±217\pm 1 , \pm \frac { 1 } { 17 } , \pm 2 , \pm \frac { 2 } { 17 }±1,±171​,±2,±172​

Question 8

Find the equation that the given graph represents.
-

Accepted Answer

A)    P(x) =−x5−20x4−100x2+100xP ( x )  = - x ^ { 5 } - 20 x ^ { 4 } - 100 x ^ { 2 } + 100 xP(x) =−x5−20x4−100x2+100x 
B)    P(x) =x5−10x4−100x2+100P ( x )  = x ^ { 5 } - 10 x ^ { 4 } - 100 x ^ { 2 } + 100P(x) =x5−10x4−100x2+100 
C)    P(x) =−x6+10x4−100x2−100P ( x )  = - x ^ { 6 } + 10 x ^ { 4 } - 100 x ^ { 2 } - 100P(x) =−x6+10x4−100x2−100 
D)    P(x) =−x6+20x4−100x2+100P ( x )  = - x ^ { 6 } + 20 x ^ { 4 } - 100 x ^ { 2 } + 100P(x) =−x6+20x4−100x2+100

Question 9

Provide an appropriate response.
-For what value of  ccc  does the quadratic function  f(x) =x2−6x+cf ( x )  = x ^ { 2 } - 6 x + cf(x) =x2−6x+c  have exactly one  xxx -intercept?

Accepted Answer

A)    32\frac { 3 } { 2 }23​ 
B)   9
C)   24
D)    −9- 9−9

Question 10

Identify the vertex of the parabola.
- f(x) =(x+8) 2f ( x )  = ( x + 8 )  ^ { 2 }f(x) =(x+8) 2

Accepted Answer

A)    (−8,0) ( - 8,0 ) (−8,0)  
B)    (8,0) ( 8,0 ) (8,0)  
C)    (0,−8) ( 0 , - 8 ) (0,−8)  
D)    (0,8) ( 0,8 ) (0,8)

Question 11

Give the equation of any oblique asymptotes.
- f(x) =2x23x2+8f ( x )  = \frac { 2 x ^ { 2 } } { 3 x ^ { 2 } + 8 }f(x) =3x2+82x2​

Accepted Answer

A)    x=y+2x = y + 2x=y+2 
B)   none
C)    y=x+2y = x + 2y=x+2 
D)    y=x+23y = x + \frac { 2 } { 3 }y=x+32​

Question 12

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth.
- f(x) =x3+2x2−11x−22f ( x )  = x ^ { 3 } + 2 x ^ { 2 } - 11 x - 22f(x) =x3+2x2−11x−22

Accepted Answer

A)    2,3.2,−3.22,3.2 , - 3.22,3.2,−3.2 
B)    −2,3.3,−3.3- 2,3.3 , - 3.3−2,3.3,−3.3 
C)    2,3.3,−3.32,3.3 , - 3.32,3.3,−3.3 
D)    −2,3.4,−3.4- 2,3.4 , - 3.4−2,3.4,−3.4

Question 13

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth.
- f(x) =2x3+x2−14x−7f ( x )  = 2 x ^ { 3 } + x ^ { 2 } - 14 x - 7f(x) =2x3+x2−14x−7

Accepted Answer

A)    −0.5,2.6,−2.6- 0.5,2.6 , - 2.6−0.5,2.6,−2.6 
B)    0.5,2.6,−2.60.5,2.6 , - 2.60.5,2.6,−2.6 
C)    −2,2.7,−2.7- 2,2.7 , - 2.7−2,2.7,−2.7 
D)    2,7,−72,7 , - 72,7,−7

Question 14

Find an equation for the rational function graph.
-

Accepted Answer

A)    f(x) =(x+2) 2(x+4) (x+2) f ( x )  = \frac { ( x + 2 )  ^ { 2 } } { ( x + 4 )  ( x + 2 )  }f(x) =(x+4) (x+2) (x+2) 2​ 
B)    f(x) =x−2x−4f ( x )  = \frac { x - 2 } { x - 4 }f(x) =x−4x−2​ 
C)    f(x) =(x−4) (x−2) (x−2) 2f ( x )  = \frac { ( x - 4 )  ( x - 2 )  } { ( x - 2 )  ^ { 2 } }f(x) =(x−2) 2(x−4) (x−2) ​ 
D)    f(x) =(x−2) 2(x−4) (x−2) f ( x )  = \frac { ( x - 2 )  ^ { 2 } } { ( x - 4 )  ( x - 2 )  }f(x) =(x−4) (x−2) (x−2) 2​

Question 15

x varies inversely as v, and x=45 when v=5. Find x when v=25. x 	ext { varies inversely as } v 	ext {, and } x = 45 	ext { when } v = 5 	ext {. Find } x 	ext { when } v = 25 	ext {. }x varies inversely as v, and x=45 when v=5. Find x when v=25.

Accepted Answer

A)   25
B)   5
C)   45
D)   9

Question 16

Identify the vertex of the parabola.
- y=x2+5y = x ^ { 2 } + 5y=x2+5

Accepted Answer

A)    (5,0) ( 5,0 ) (5,0)  
B)    (−5,0) ( - 5,0 ) (−5,0)  
C)    (0,5) ( 0,5 ) (0,5)  
D)    (0,−5) ( 0 , - 5 ) (0,−5)

Question 17

A rock is propelled upward from the top of a building 170 feet tall at an initial velocity of 168 feet per second. The function that describes the height of the rocket in terms of time t is  s(t) =−16t2+168t+170s ( t )  = - 16 t ^ { 2 } + 168 t + 170s(t) =−16t2+168t+170  Determine the
Maximum height that the rock reaches.

Accepted Answer

A)   630 ft
B)   592 ft
C)   579 ft
D)   611 ft

Question 18

Sketch the graph of the polynomial function.
- f(x) =−14x2f ( x )  = - \frac { 1 } { 4 } x ^ { 2 }f(x) =−41​x2

Accepted Answer

A)  
B)  
C)  
D)

Question 19

Round to the nearest tenth unless indicated otherwise.
-The volume of wood in a tree varies jointly as the height of the tree and the square of the distance around the tree trunk. If the volume of wood is 15.84 cubic feet when the height is 22 feet and the distance around the trunk
Is 3 feet, what is the volume of wood obtained from a tree that is 23 feet tall having a measurement of 4 feet
Around the trunk?

Accepted Answer

A)    33.4ft333.4 \mathrm { ft } ^ { 3 }33.4ft3 
B)    21.4ft321.4 \mathrm { ft } ^ { 3 }21.4ft3 
C)    29.4ft329.4 \mathrm { ft } ^ { 3 }29.4ft3 
D)    38.4ft338.4 \mathrm { ft } ^ { 3 }38.4ft3

Question 20

Use synthetic division to decide whether the given number k is a zero of the given polynomial function.
-$k = - 1 - 3 i ; f ( x ) = x ^ { 2 } - 2 x + 10$

Accepted Answer

A) True 
 B)False

Exam 4: Polynomials and Rational Functions

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. - $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 11 x - 22$

Correct Answer
verified

Given the equation or other information for a parabola, find the matching description or graph. - $\begin{array} { l } f ( x ) = a x ^ { 2 } + b x + c \\a > 0 ; b ^ { 2 } - 4 a c > 0\end{array}$

Correct Answer
verified

A rock is propelled upward from the top of a building 170 feet tall at an initial velocity of 168 feet per second. The function that describes the height of the rocket in terms of time t is $s ( t ) = - 16 t ^ { 2 } + 168 t + 170$ Determine the Maximum height that the rock reaches.

Correct Answer
verified

Correct Answer
verified

Sketch the graph of the polynomial function. - $f ( x ) = - \frac { 1 } { 4 } x ^ { 2 }$ $Sketch the graph of the polynomial function. - f ( x ) = - \frac { 1 } { 4 } x ^ { 2 } A) B) C) D)$

Correct Answer
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Provide an appropriate response. -For what value of $c$ does the quadratic function $f ( x ) = x ^ { 2 } - 6 x + c$ have exactly one $x$ -intercept?

Correct Answer
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Identify the vertex of the parabola. - $f ( x ) = ( x + 8 ) ^ { 2 }$

Correct Answer
verified

Correct Answer
verified

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $- 3 , - 1,4$ and $P ( 2 ) = 5$

Correct Answer
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Determine which of the rational functions given below has the following feature(s) . -The x-intercept is (2, 0)

Correct Answer
verified

Give the equation of any oblique asymptotes. - $f ( x ) = \frac { 2 x ^ { 2 } } { 3 x ^ { 2 } + 8 }$

Correct Answer
verified

Determine whether the statement is true or false. - $\text { The function } f ( x ) = \frac { 1 } { x } \text { is decreasing on the interval } ( 0 , \infty )$

Correct Answer
verified

Find a polynomial of least degree with only real coefficients and having the given zeros. - $1 - \sqrt { 3 } , 1 + \sqrt { 3 }$ , and $1 + i$

Correct Answer
verified

Correct Answer
verified

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. - $f ( x ) = 2 x ^ { 3 } + x ^ { 2 } - 14 x - 7$

Correct Answer
verified

Give all possible rational zeros for the following polynomial. - $P ( x ) = 2 x ^ { 3 } - 5 x ^ { 2 } + 7 x - 17$

Correct Answer
verified

Sketch the graph of the polynomial function. - $f ( x ) = \frac { 1 } { 3 } ( x + 2 ) ^ { 4 } + 3$ $Sketch the graph of the polynomial function. - f ( x ) = \frac { 1 } { 3 } ( x + 2 ) ^ { 4 } + 3 A) B) C) D)$

Correct Answer
verified

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = - 1 - 3 i ; f ( x ) = x ^ { 2 } - 2 x + 10$

Correct Answer
verified

$x \text { varies inversely as } v \text {, and } x = 45 \text { when } v = 5 \text {. Find } x \text { when } v = 25 \text {. }$

Correct Answer
verified

Identify the vertex of the parabola. - $y = x ^ { 2 } + 5$

Correct Answer
verified

Exam 4: Polynomials and Rational Functions

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. - f(x) =x3+2x2−11x−22f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 11 x - 22f(x) =x3+2x2−11x−22

Correct AnswerverifiedShow Answer

Given the equation or other information for a parabola, find the matching description or graph. - f(x) =ax2+bx+ca>0;b2−4ac>0\begin{array} { l } f ( x ) = a x ^ { 2 } + b x + c \\a > 0 ; b ^ { 2 } - 4 a c > 0\end{array}f(x) =ax2+bx+ca>0;b2−4ac>0​

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Find the equation that the given graph represents. -

Correct AnswerverifiedShow Answer

Sketch the graph of the polynomial function. - f(x) =−14x2f ( x ) = - \frac { 1 } { 4 } x ^ { 2 }f(x) =−41​x2

Correct AnswerverifiedShow Answer

Provide an appropriate response. -For what value of ccc does the quadratic function f(x) =x2−6x+cf ( x ) = x ^ { 2 } - 6 x + cf(x) =x2−6x+c have exactly one xxx -intercept?

Correct AnswerverifiedShow Answer

Identify the vertex of the parabola. - f(x) =(x+8) 2f ( x ) = ( x + 8 ) ^ { 2 }f(x) =(x+8) 2

Correct AnswerverifiedShow Answer

Find an equation for the rational function graph. -

Correct AnswerverifiedShow Answer

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of −3,−1,4- 3 , - 1,4−3,−1,4 and P(2) =5P ( 2 ) = 5P(2) =5

Correct AnswerverifiedShow Answer

Determine which of the rational functions given below has the following feature(s) . -The x-intercept is (2, 0)

Correct AnswerverifiedShow Answer

Give the equation of any oblique asymptotes. - f(x) =2x23x2+8f ( x ) = \frac { 2 x ^ { 2 } } { 3 x ^ { 2 } + 8 }f(x) =3x2+82x2​

Correct AnswerverifiedShow Answer

Determine whether the statement is true or false. - The function f(x)=1x is decreasing on the interval (0,∞)\text { The function } f ( x ) = \frac { 1 } { x } \text { is decreasing on the interval } ( 0 , \infty ) The function f(x)=x1​ is decreasing on the interval (0,∞)

Correct AnswerverifiedShow Answer

Find a polynomial of least degree with only real coefficients and having the given zeros. - 1−3,1+31 - \sqrt { 3 } , 1 + \sqrt { 3 }1−3​,1+3​ , and 1+i1 + i1+i

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. - f(x) =2x3+x2−14x−7f ( x ) = 2 x ^ { 3 } + x ^ { 2 } - 14 x - 7f(x) =2x3+x2−14x−7

Correct AnswerverifiedShow Answer

Give all possible rational zeros for the following polynomial. - P(x) =2x3−5x2+7x−17P ( x ) = 2 x ^ { 3 } - 5 x ^ { 2 } + 7 x - 17P(x) =2x3−5x2+7x−17

Correct AnswerverifiedShow Answer

Sketch the graph of the polynomial function. - f(x) =13(x+2) 4+3f ( x ) = \frac { 1 } { 3 } ( x + 2 ) ^ { 4 } + 3f(x) =31​(x+2) 4+3

Correct AnswerverifiedShow Answer

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - k=−1−3i;f(x)=x2−2x+10k = - 1 - 3 i ; f ( x ) = x ^ { 2 } - 2 x + 10k=−1−3i;f(x)=x2−2x+10

Correct AnswerverifiedShow Answer

x varies inversely as v, and x=45 when v=5. Find x when v=25. x \text { varies inversely as } v \text {, and } x = 45 \text { when } v = 5 \text {. Find } x \text { when } v = 25 \text {. }x varies inversely as v, and x=45 when v=5. Find x when v=25.

Correct AnswerverifiedShow Answer

Identify the vertex of the parabola. - y=x2+5y = x ^ { 2 } + 5y=x2+5

Correct AnswerverifiedShow Answer

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. - $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 11 x - 22$

Correct Answer
verified

Given the equation or other information for a parabola, find the matching description or graph. - $\begin{array} { l } f ( x ) = a x ^ { 2 } + b x + c \\a > 0 ; b ^ { 2 } - 4 a c > 0\end{array}$

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Sketch the graph of the polynomial function. - $f ( x ) = - \frac { 1 } { 4 } x ^ { 2 }$ $Sketch the graph of the polynomial function. - f ( x ) = - \frac { 1 } { 4 } x ^ { 2 } A) B) C) D)$

Correct Answer
verified

Provide an appropriate response. -For what value of $c$ does the quadratic function $f ( x ) = x ^ { 2 } - 6 x + c$ have exactly one $x$ -intercept?

Correct Answer
verified

Identify the vertex of the parabola. - $f ( x ) = ( x + 8 ) ^ { 2 }$

Correct Answer
verified

Correct Answer
verified

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $- 3 , - 1,4$ and $P ( 2 ) = 5$

Correct Answer
verified

Correct Answer
verified

Give the equation of any oblique asymptotes. - $f ( x ) = \frac { 2 x ^ { 2 } } { 3 x ^ { 2 } + 8 }$

Correct Answer
verified

Determine whether the statement is true or false. - $\text { The function } f ( x ) = \frac { 1 } { x } \text { is decreasing on the interval } ( 0 , \infty )$

Correct Answer
verified

Find a polynomial of least degree with only real coefficients and having the given zeros. - $1 - \sqrt { 3 } , 1 + \sqrt { 3 }$ , and $1 + i$

Correct Answer
verified

Correct Answer
verified

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. - $f ( x ) = 2 x ^ { 3 } + x ^ { 2 } - 14 x - 7$

Correct Answer
verified

Give all possible rational zeros for the following polynomial. - $P ( x ) = 2 x ^ { 3 } - 5 x ^ { 2 } + 7 x - 17$

Correct Answer
verified

Sketch the graph of the polynomial function. - $f ( x ) = \frac { 1 } { 3 } ( x + 2 ) ^ { 4 } + 3$ $Sketch the graph of the polynomial function. - f ( x ) = \frac { 1 } { 3 } ( x + 2 ) ^ { 4 } + 3 A) B) C) D)$

Correct Answer
verified

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = - 1 - 3 i ; f ( x ) = x ^ { 2 } - 2 x + 10$

Correct Answer
verified

$x \text { varies inversely as } v \text {, and } x = 45 \text { when } v = 5 \text {. Find } x \text { when } v = 25 \text {. }$

Correct Answer
verified

Identify the vertex of the parabola. - $y = x ^ { 2 } + 5$

Correct Answer
verified