Question 1

Find the vertical asymptote(s) of the graph of the given function.
-$$g ( x ) = \frac { x + 7 } { x - 3 }$$

Accepted Answer

A)  $x = - 7$ 
B)  $x = 3$ 
C)  $x = - 3$ 
D)  $y = 3$ 
A)  $x = - 7$ 
B)  $x = 3$ 
C)  $x = - 3$ 
D)  $y = 3$ B

Question 2

Use the leading-term test to match the function with the correct graph.
-$$f ( x ) = - 0.3 x ^ { 7 } + 0.14 x ^ { 6 } - 0.13 x ^ { 5 } + x ^ { 4 } + x ^ { 3 } - 8 x - 5$$

Accepted Answer

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

Question 3

Find the horizontal asymptote, if any, of the rational function.
-$$f ( x ) = \frac { 3 x ^ { 3 } - 9 x - 7 } { 7 x ^ { 3 } - 5 x + 2 }$$

Accepted Answer

A)  $y = \frac { 3 } { 7 }$ 
B)  $y = \frac { 9 } { 5 }$ 
C)  $\mathrm { y } = 0$ 
D)  None 
A)  $y = \frac { 3 } { 7 }$ 
B)  $y = \frac { 9 } { 5 }$ 
C)  $\mathrm { y } = 0$ 
D)  None A

Question 4

Graph the function, showing all asymptotes (those that do not correspond to an axis) as dashed lines. List the x- and
y-intercepts.
-$$f ( x ) = \frac { x ^ { 2 } - 3 x - 4 } { 3 x ^ { 2 } + 2 }$$

Accepted Answer

A)  No $x$-intercepts, $y$-intercept: $( 0 , - 4 )$;
  
B)  No $x$-intercepts, $y$-intercept: $( 0 , - 4 )$;
  
C)  x-intercepts: $( 1,0 )$ and $( - 4,0 )$,
  
D)  x-intercepts: $( - 1,0 )$ and $( 4,0 )$, y-intercept: $( 0 , - 2 )$; $\mathrm { y }$-intercept: $( 0 , - 2 )$;
  
A)  No $x$-intercepts, $y$-intercept: $( 0 , - 4 )$;
  
B)  No $x$-intercepts, $y$-intercept: $( 0 , - 4 )$;
  
C)  x-intercepts: $( 1,0 )$ and $( - 4,0 )$,
  
D)  x-intercepts: $( - 1,0 )$ and $( 4,0 )$, y-intercept: $( 0 , - 2 )$; $\mathrm { y }$-intercept: $( 0 , - 2 )$;

Question 5

Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative
real zeros for the function.
-$$P ( x ) = - 4 x ^ { 4 } - 3 x ^ { 3 } - 7 x ^ { 2 } - 4 x + 7$$

Accepted Answer

A)  0 or 2 positive; 1 or 3 negative 
B)  1 positive; 2 negative 
C)  1 positive; 1 or 3 negative 
D)  1 positive; 1 negative 
A)  0 or 2 positive; 1 or 3 negative 
B)  1 positive; 2 negative 
C)  1 positive; 1 or 3 negative 
D)  1 positive; 1 negative

Question 6

Provide the requested response.
-Suppose that a polynomial function of degree 5 with rational coefficients has $- 5,4 , - 3,5 - i$ as zeros. Find the other zero(s).

Accepted Answer

A)  $5 + i$ 
B)  $- 5 - \mathrm { i }$ 
C)  $5 , - 4,3,5 + \mathrm { i }$ 
D)  $- 5 + \mathrm { i }$ 
A)  $5 + i$ 
B)  $- 5 - \mathrm { i }$ 
C)  $5 , - 4,3,5 + \mathrm { i }$ 
D)  $- 5 + \mathrm { i }$

Question 7

Find the requested polynomial.
-Find a polynomial function of degree 3 with $- 4,0 , \frac { 1 } { 2 }$ as zeros.

Accepted Answer

A)  $f ( x ) = x ^ { 3 } - \frac { 7 } { 2 } x ^ { 2 } + 2 x$ 
B)  $f ( x ) = x ^ { 3 } + \frac { 9 } { 2 } x ^ { 2 } - 2 x$ 
C)  $f ( x ) = x ^ { 3 } - \frac { 7 } { 2 } x ^ { 2 } - 2 x$ 
D)  $f ( x ) = x ^ { 3 } + \frac { 7 } { 2 } x ^ { 2 } - 2 x$ 
A)  $f ( x ) = x ^ { 3 } - \frac { 7 } { 2 } x ^ { 2 } + 2 x$ 
B)  $f ( x ) = x ^ { 3 } + \frac { 9 } { 2 } x ^ { 2 } - 2 x$ 
C)  $f ( x ) = x ^ { 3 } - \frac { 7 } { 2 } x ^ { 2 } - 2 x$ 
D)  $f ( x ) = x ^ { 3 } + \frac { 7 } { 2 } x ^ { 2 } - 2 x$

Question 8

Use long division to determine whether the binomial is a factor of f(x).
-$$f ( x ) = x ^ { 4 } - x ^ { 3 } - 3 x ^ { 2 } + 4 x + 7 ; x + 2$$

Accepted Answer

A)  Yes 
B)  $\mathrm { No }$ 
A)  Yes 
B)  $\mathrm { No }$

Question 9

Use synthetic division to find the quotient and the remainder.
-$$\left( 3 x ^ { 4 } + 2 x ^ { 2 } - 1 \right) \div \left( x + \frac { 1 } { 2 } \right)$$

Accepted Answer

A)  $Q ( x ) = 3 x ^ { 3 } + \frac { 3 } { 2 } x ^ { 2 } - \frac { 11 } { 8 } x + \frac { 11 } { 8 } ; R ( x ) = - \frac { 5 } { 16 }$ 
B)  $Q ( x ) = 3 x ^ { 3 } - 1 ; R ( x ) = - 2$ 
C)  $Q ( x ) = 3 x ^ { 3 } - 1 ; R ( x ) = 0$ 
D)  $Q ( x ) = 3 x ^ { 3 } - \frac { 3 } { 2 } x ^ { 2 } + \frac { 11 } { 4 } x - \frac { 11 } { 8 } ; R ( x ) = - \frac { 5 } { 16 }$ 
A)  $Q ( x ) = 3 x ^ { 3 } + \frac { 3 } { 2 } x ^ { 2 } - \frac { 11 } { 8 } x + \frac { 11 } { 8 } ; R ( x ) = - \frac { 5 } { 16 }$ 
B)  $Q ( x ) = 3 x ^ { 3 } - 1 ; R ( x ) = - 2$ 
C)  $Q ( x ) = 3 x ^ { 3 } - 1 ; R ( x ) = 0$ 
D)  $Q ( x ) = 3 x ^ { 3 } - \frac { 3 } { 2 } x ^ { 2 } + \frac { 11 } { 4 } x - \frac { 11 } { 8 } ; R ( x ) = - \frac { 5 } { 16 }$

Question 10

Graph the function.
-$$f ( x ) = x ^ { 3 } - 3 x ^ { 2 }$$

Accepted Answer

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

Question 11

Use the leading-term test to match the function with the correct graph.
-$$f ( x ) = x ^ { 5 } - x ^ { 3 } + x ^ { 2 } + 4$$

Accepted Answer

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

Question 12

Sketch the graph of the polynomial function. Use the rational zeros theorem when finding the zeros.
-$$f ( x ) = 2 x ^ { 3 } + x ^ { 2 } - 13 x + 6$$

Accepted Answer

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

Question 13

Solve.
-The profit made when $t$ units are sold is given by $P = t ^ { 2 } - 24 t + 140$ for $t > 0$. Determine the values of $t$ for which $P < 0$ (a loss is taken).

Accepted Answer

A)  $( 10,14 )$ 
B)  $( 0 , \infty )$ 
C)  $[ 10,14 ]$ 
D)  $( - \infty , 10 ) \cup ( 14 , \infty )$ 
A)  $( 10,14 )$ 
B)  $( 0 , \infty )$ 
C)  $[ 10,14 ]$ 
D)  $( - \infty , 10 ) \cup ( 14 , \infty )$

Question 14

Solve.
-$x ^ { 3 } + 5 x ^ { 2 } - 4 x - 20 \geq 0$

Accepted Answer

A)  $[ - 5 , \infty )$ 
B)  $[ - 5 , - 2 ] \cup [ 2 , \infty )$ 
C)  $[ - 2,2 ] \cup [ 5 , \infty )$ 
D)  $[ - 5,2 ]$ 
A)  $[ - 5 , \infty )$ 
B)  $[ - 5 , - 2 ] \cup [ 2 , \infty )$ 
C)  $[ - 2,2 ] \cup [ 5 , \infty )$ 
D)  $[ - 5,2 ]$

Question 15

Find only the rational zeros.
-$$f ( x ) = x ^ { 4 } - 8 x ^ { 3 } + 4 x ^ { 2 } + 24 x - 21$$

Accepted Answer

A)  $- 7,1$ 
B)  7,1 
C)  $7 , - 1$ 
D)  No rational zeros 
A)  $- 7,1$ 
B)  7,1 
C)  $7 , - 1$ 
D)  No rational zeros

Question 16

Solve.
-$$x ^ { 2 } + 10 x + 25 \leq 0$$

Accepted Answer

A)  $[ 5 , \infty )$ 
B)  $\{ 5 \}$ 
C)  $( - \infty , - 5 ] \cup [ - 5 , \infty )$ 
D)  $\{ - 5 \}$ 
A)  $[ 5 , \infty )$ 
B)  $\{ 5 \}$ 
C)  $( - \infty , - 5 ] \cup [ - 5 , \infty )$ 
D)  $\{ - 5 \}$

Question 17

Solve the inequality.
-For the function $h ( x ) = \frac { 2 x } { ( x - 2 ) ( x - 6 ) }$, solve $h ( x ) < 0$.

Accepted Answer

A)  $( - \infty , 2 ) \cup ( 6 , \infty )$ 
B)  $( - \infty , 0 ) \cup ( 2,6 )$ 
C)  $[ 2,6 ]$ 
D)  $( - \infty , 2 ] \cup [ 6 , \infty )$ 
A)  $( - \infty , 2 ) \cup ( 6 , \infty )$ 
B)  $( - \infty , 0 ) \cup ( 2,6 )$ 
C)  $[ 2,6 ]$ 
D)  $( - \infty , 2 ] \cup [ 6 , \infty )$

Question 18

Find the correct end behavior diagram for the given polynomial function.
-$$f ( x ) = - x ^ { 6 } + 3 x ^ { 5 } - x ^ { 2 } - 4 x + 3$$

Accepted Answer

The answer of Find the correct end behavior diagram for...

Question 19

Provide the requested response.
-Suppose that a polynomial function of degree 4 with rational coefficients has 6, 4, 3i as zeros. Find the other zero.

Accepted Answer

A) 3- i 
B) - 3i 
C) -6 $$\text { 
D)  } \sqrt { 3 } \mathrm { i }$$ 
A) 3- i 
B) - 3i 
C) -6 $$\text { 
D)  } \sqrt { 3 } \mathrm { i }$$

Question 20

Solve the inequality.
-For the function $f ( x ) = x ^ { 2 } - 2 x - 35$, solve $f ( x ) \leq 0$.

Accepted Answer

A)  $( - \infty , - 5 ] \cup [ 7 , \infty )$ 
B)  $[ - 5,7 ]$ 
C)  $( - \infty , - 5 ]$ 
D)  $[ 7 , \infty )$ 
A)  $( - \infty , - 5 ] \cup [ 7 , \infty )$ 
B)  $[ - 5,7 ]$ 
C)  $( - \infty , - 5 ]$ 
D)  $[ 7 , \infty )$

Find the vertical asymptote(s) of the graph of the given function. - $g ( x ) = \frac { x + 7 } { x - 3 }$

Use the leading-term test to match the function with the correct graph. - $f ( x ) = - 0.3 x ^ { 7 } + 0.14 x ^ { 6 } - 0.13 x ^ { 5 } + x ^ { 4 } + x ^ { 3 } - 8 x - 5$

Find the horizontal asymptote, if any, of the rational function. - $f ( x ) = \frac { 3 x ^ { 3 } - 9 x - 7 } { 7 x ^ { 3 } - 5 x + 2 }$

Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative real zeros for the function. - $P ( x ) = - 4 x ^ { 4 } - 3 x ^ { 3 } - 7 x ^ { 2 } - 4 x + 7$

Provide the requested response. -Suppose that a polynomial function of degree 5 with rational coefficients has $- 5,4 , - 3,5 - i$ as zeros. Find the other zero(s).

Find the requested polynomial. -Find a polynomial function of degree 3 with $- 4,0 , \frac { 1 } { 2 }$ as zeros.

Use long division to determine whether the binomial is a factor of f(x). - $f ( x ) = x ^ { 4 } - x ^ { 3 } - 3 x ^ { 2 } + 4 x + 7 ; x + 2$

Use synthetic division to find the quotient and the remainder. - $\left( 3 x ^ { 4 } + 2 x ^ { 2 } - 1 \right) \div \left( x + \frac { 1 } { 2 } \right)$

Graph the function. - $f ( x ) = x ^ { 3 } - 3 x ^ { 2 }$ $Graph the function. - f ( x ) = x ^ { 3 } - 3 x ^ { 2 }$

Use the leading-term test to match the function with the correct graph. - $f ( x ) = x ^ { 5 } - x ^ { 3 } + x ^ { 2 } + 4$

Sketch the graph of the polynomial function. Use the rational zeros theorem when finding the zeros. - $f ( x ) = 2 x ^ { 3 } + x ^ { 2 } - 13 x + 6$ $Sketch the graph of the polynomial function. Use the rational zeros theorem when finding the zeros. - f ( x ) = 2 x ^ { 3 } + x ^ { 2 } - 13 x + 6$

Solve. -The profit made when $t$ units are sold is given by $P = t ^ { 2 } - 24 t + 140$ for $t > 0$ . Determine the values of $t$ for which $P < 0$ (a loss is taken).

Solve. - $x ^ { 3 } + 5 x ^ { 2 } - 4 x - 20 \geq 0$

Find only the rational zeros. - $f ( x ) = x ^ { 4 } - 8 x ^ { 3 } + 4 x ^ { 2 } + 24 x - 21$

Solve. - $x ^ { 2 } + 10 x + 25 \leq 0$

Solve the inequality. -For the function $h ( x ) = \frac { 2 x } { ( x - 2 ) ( x - 6 ) }$ , solve $h ( x ) < 0$ .

Find the correct end behavior diagram for the given polynomial function. - $f ( x ) = - x ^ { 6 } + 3 x ^ { 5 } - x ^ { 2 } - 4 x + 3$ $Find the correct end behavior diagram for the given polynomial function. - f ( x ) = - x ^ { 6 } + 3 x ^ { 5 } - x ^ { 2 } - 4 x + 3$

Provide the requested response. -Suppose that a polynomial function of degree 4 with rational coefficients has 6, 4, 3i as zeros. Find the other zero.

Solve the inequality. -For the function $f ( x ) = x ^ { 2 } - 2 x - 35$ , solve $f ( x ) \leq 0$ .

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Exam 4: Polynomial and Rational Functions

Find the vertical asymptote(s) of the graph of the given function. - g(x)=x+7x−3g ( x ) = \frac { x + 7 } { x - 3 }g(x)=x−3x+7​

Use the leading-term test to match the function with the correct graph. - f(x)=−0.3x7+0.14x6−0.13x5+x4+x3−8x−5f ( x ) = - 0.3 x ^ { 7 } + 0.14 x ^ { 6 } - 0.13 x ^ { 5 } + x ^ { 4 } + x ^ { 3 } - 8 x - 5f(x)=−0.3x7+0.14x6−0.13x5+x4+x3−8x−5

Find the horizontal asymptote, if any, of the rational function. - f(x)=3x3−9x−77x3−5x+2f ( x ) = \frac { 3 x ^ { 3 } - 9 x - 7 } { 7 x ^ { 3 } - 5 x + 2 }f(x)=7x3−5x+23x3−9x−7​

Graph the function, showing all asymptotes (those that do not correspond to an axis) as dashed lines. List the x- and y-intercepts. - f(x)=x2−3x−43x2+2f ( x ) = \frac { x ^ { 2 } - 3 x - 4 } { 3 x ^ { 2 } + 2 }f(x)=3x2+2x2−3x−4​

Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative real zeros for the function. - P(x)=−4x4−3x3−7x2−4x+7P ( x ) = - 4 x ^ { 4 } - 3 x ^ { 3 } - 7 x ^ { 2 } - 4 x + 7P(x)=−4x4−3x3−7x2−4x+7

Provide the requested response. -Suppose that a polynomial function of degree 5 with rational coefficients has −5,4,−3,5−i- 5,4 , - 3,5 - i−5,4,−3,5−i as zeros. Find the other zero(s).

Find the requested polynomial. -Find a polynomial function of degree 3 with −4,0,12- 4,0 , \frac { 1 } { 2 }−4,0,21​ as zeros.

Use long division to determine whether the binomial is a factor of f(x). - f(x)=x4−x3−3x2+4x+7;x+2f ( x ) = x ^ { 4 } - x ^ { 3 } - 3 x ^ { 2 } + 4 x + 7 ; x + 2f(x)=x4−x3−3x2+4x+7;x+2

Use synthetic division to find the quotient and the remainder. - (3x4+2x2−1)÷(x+12)\left( 3 x ^ { 4 } + 2 x ^ { 2 } - 1 \right) \div \left( x + \frac { 1 } { 2 } \right)(3x4+2x2−1)÷(x+21​)

Graph the function. - f(x)=x3−3x2f ( x ) = x ^ { 3 } - 3 x ^ { 2 }f(x)=x3−3x2

Use the leading-term test to match the function with the correct graph. - f(x)=x5−x3+x2+4f ( x ) = x ^ { 5 } - x ^ { 3 } + x ^ { 2 } + 4f(x)=x5−x3+x2+4

Sketch the graph of the polynomial function. Use the rational zeros theorem when finding the zeros. - f(x)=2x3+x2−13x+6f ( x ) = 2 x ^ { 3 } + x ^ { 2 } - 13 x + 6f(x)=2x3+x2−13x+6

Solve. -The profit made when ttt units are sold is given by P=t2−24t+140P = t ^ { 2 } - 24 t + 140P=t2−24t+140 for t>0t > 0t>0 . Determine the values of ttt for which P<0P < 0P<0 (a loss is taken).

Solve. - x3+5x2−4x−20≥0x ^ { 3 } + 5 x ^ { 2 } - 4 x - 20 \geq 0x3+5x2−4x−20≥0

Find only the rational zeros. - f(x)=x4−8x3+4x2+24x−21f ( x ) = x ^ { 4 } - 8 x ^ { 3 } + 4 x ^ { 2 } + 24 x - 21f(x)=x4−8x3+4x2+24x−21

Solve. - x2+10x+25≤0x ^ { 2 } + 10 x + 25 \leq 0x2+10x+25≤0

Solve the inequality. -For the function h(x)=2x(x−2)(x−6)h ( x ) = \frac { 2 x } { ( x - 2 ) ( x - 6 ) }h(x)=(x−2)(x−6)2x​ , solve h(x)<0h ( x ) < 0h(x)<0 .

Find the correct end behavior diagram for the given polynomial function. - f(x)=−x6+3x5−x2−4x+3f ( x ) = - x ^ { 6 } + 3 x ^ { 5 } - x ^ { 2 } - 4 x + 3f(x)=−x6+3x5−x2−4x+3

Provide the requested response. -Suppose that a polynomial function of degree 4 with rational coefficients has 6, 4, 3i as zeros. Find the other zero.

Solve the inequality. -For the function f(x)=x2−2x−35f ( x ) = x ^ { 2 } - 2 x - 35f(x)=x2−2x−35 , solve f(x)≤0f ( x ) \leq 0f(x)≤0 .

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Find the vertical asymptote(s) of the graph of the given function. - $g ( x ) = \frac { x + 7 } { x - 3 }$

Use the leading-term test to match the function with the correct graph. - $f ( x ) = - 0.3 x ^ { 7 } + 0.14 x ^ { 6 } - 0.13 x ^ { 5 } + x ^ { 4 } + x ^ { 3 } - 8 x - 5$

Find the horizontal asymptote, if any, of the rational function. - $f ( x ) = \frac { 3 x ^ { 3 } - 9 x - 7 } { 7 x ^ { 3 } - 5 x + 2 }$

Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative real zeros for the function. - $P ( x ) = - 4 x ^ { 4 } - 3 x ^ { 3 } - 7 x ^ { 2 } - 4 x + 7$

Provide the requested response. -Suppose that a polynomial function of degree 5 with rational coefficients has $- 5,4 , - 3,5 - i$ as zeros. Find the other zero(s).

Find the requested polynomial. -Find a polynomial function of degree 3 with $- 4,0 , \frac { 1 } { 2 }$ as zeros.

Use long division to determine whether the binomial is a factor of f(x). - $f ( x ) = x ^ { 4 } - x ^ { 3 } - 3 x ^ { 2 } + 4 x + 7 ; x + 2$

Use synthetic division to find the quotient and the remainder. - $\left( 3 x ^ { 4 } + 2 x ^ { 2 } - 1 \right) \div \left( x + \frac { 1 } { 2 } \right)$

Graph the function. - $f ( x ) = x ^ { 3 } - 3 x ^ { 2 }$ $Graph the function. - f ( x ) = x ^ { 3 } - 3 x ^ { 2 }$

Use the leading-term test to match the function with the correct graph. - $f ( x ) = x ^ { 5 } - x ^ { 3 } + x ^ { 2 } + 4$

Sketch the graph of the polynomial function. Use the rational zeros theorem when finding the zeros. - $f ( x ) = 2 x ^ { 3 } + x ^ { 2 } - 13 x + 6$ $Sketch the graph of the polynomial function. Use the rational zeros theorem when finding the zeros. - f ( x ) = 2 x ^ { 3 } + x ^ { 2 } - 13 x + 6$

Solve. -The profit made when $t$ units are sold is given by $P = t ^ { 2 } - 24 t + 140$ for $t > 0$ . Determine the values of $t$ for which $P < 0$ (a loss is taken).

Solve. - $x ^ { 3 } + 5 x ^ { 2 } - 4 x - 20 \geq 0$

Find only the rational zeros. - $f ( x ) = x ^ { 4 } - 8 x ^ { 3 } + 4 x ^ { 2 } + 24 x - 21$

Solve. - $x ^ { 2 } + 10 x + 25 \leq 0$

Solve the inequality. -For the function $h ( x ) = \frac { 2 x } { ( x - 2 ) ( x - 6 ) }$ , solve $h ( x ) < 0$ .

Find the correct end behavior diagram for the given polynomial function. - $f ( x ) = - x ^ { 6 } + 3 x ^ { 5 } - x ^ { 2 } - 4 x + 3$ $Find the correct end behavior diagram for the given polynomial function. - f ( x ) = - x ^ { 6 } + 3 x ^ { 5 } - x ^ { 2 } - 4 x + 3$

Solve the inequality. -For the function $f ( x ) = x ^ { 2 } - 2 x - 35$ , solve $f ( x ) \leq 0$ .