Question 1

Find all zeros of the function and write the polynomial as a product of linear factors.
-$$f ( x ) = x ^ { 3 } + 11 x ^ { 2 } + 36 x + 26$$

Accepted Answer

A)  $f ( x ) = ( x + 1 ) ( x + 5 + i \sqrt { 2 } ) ( x - 1 - i \sqrt { 2 } )$ 
B)  $f ( x ) = ( x + 1 ) ( x + 5 + i ) ( x + 5 - i )$ 
C)  $f ( x ) = ( x + 1 ) ( x + 5 + i ) ( x - 5 - i )$ 
D)  $f ( x ) = ( x - 1 ) ( x + 5 + i \sqrt { 2 } ) ( x + 5 - i \sqrt { 2 } )$ 
A)  $f ( x ) = ( x + 1 ) ( x + 5 + i \sqrt { 2 } ) ( x - 1 - i \sqrt { 2 } )$ 
B)  $f ( x ) = ( x + 1 ) ( x + 5 + i ) ( x + 5 - i )$ 
C)  $f ( x ) = ( x + 1 ) ( x + 5 + i ) ( x - 5 - i )$ 
D)  $f ( x ) = ( x - 1 ) ( x + 5 + i \sqrt { 2 } ) ( x + 5 - i \sqrt { 2 } )$

Question 2

Choose the one alternative that best completes the statement or answers the question.
Find the domain of the rational function.
-$$g ( x ) = \frac { x + 8 } { x ^ { 2 } - 49 x }$$

Accepted Answer

A)  $\{ x \mid x \neq - 7,7 , - 8 \}$ 
B)  $\{ x | x \neq - 7,7 |$ 
C)  $\{ x \mid x \neq 0,49 \}$ 
D)  all real numbers 
A)  $\{ x \mid x \neq - 7,7 , - 8 \}$ 
B)  $\{ x | x \neq - 7,7 |$ 
C)  $\{ x \mid x \neq 0,49 \}$ 
D)  all real numbers

Question 3

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the
zeros to factor f over the real numbers.
-$$f ( x ) = 4 x ^ { 3 } + 19 x ^ { 2 } - 8 x + 15$$

Accepted Answer

A)  $1 , \frac { 4 } { 3 } , - 5 ; f ( x ) = ( 4 x - 3 ) ( x - 1 ) ( x + 5 )$ 
B)  $- 5 , \frac { 3 } { 4 } , 1 ; f ( x ) = ( 4 x - 3 ) ( x - 1 ) ( x + 5 )$ 
C)  $- 1 , \frac { 4 } { 3 } , - 5 ; f ( x ) = ( 4 x - 3 ) ( x - 5 ) ( x + 1 )$ 
D)  $- 1 , \frac { 3 } { 4 } , 5 ; f ( x ) = ( 4 x - 3 ) ( x - 5 ) ( x + 1 )$ 
A)  $1 , \frac { 4 } { 3 } , - 5 ; f ( x ) = ( 4 x - 3 ) ( x - 1 ) ( x + 5 )$ 
B)  $- 5 , \frac { 3 } { 4 } , 1 ; f ( x ) = ( 4 x - 3 ) ( x - 1 ) ( x + 5 )$ 
C)  $- 1 , \frac { 4 } { 3 } , - 5 ; f ( x ) = ( 4 x - 3 ) ( x - 5 ) ( x + 1 )$ 
D)  $- 1 , \frac { 3 } { 4 } , 5 ; f ( x ) = ( 4 x - 3 ) ( x - 5 ) ( x + 1 )$

Question 4

Solve the inequality.
-$$36 \left( x ^ { 2 } - 1 \right) > 65 x$$

Accepted Answer

A)  $\left( - \frac { 4 } { 9 } , \frac { 9 } { 4 } \right)$ 
B)  $\left( - \infty , - \frac { 9 } { 4 } \right)$ or $\left( \frac { 4 } { 9 } , \infty \right)$ 
C)  $\left( - \infty , - \frac { 4 } { 9 } \right)$ or $\left( \frac { 9 } { 4 } , \infty \right)$ 
D)  $\left( - \frac { 9 } { 4 } , \frac { 4 } { 9 } \right)$ 
A)  $\left( - \frac { 4 } { 9 } , \frac { 9 } { 4 } \right)$ 
B)  $\left( - \infty , - \frac { 9 } { 4 } \right)$ or $\left( \frac { 4 } { 9 } , \infty \right)$ 
C)  $\left( - \infty , - \frac { 4 } { 9 } \right)$ or $\left( \frac { 9 } { 4 } , \infty \right)$ 
D)  $\left( - \frac { 9 } { 4 } , \frac { 4 } { 9 } \right)$

Question 5

Solve the inequality.
-$$x ^ { 2 } - 8 x + 7 > 0$$

Accepted Answer

A)  $( 1,7 )$ 
B)  $( - \infty , 1 )$ 
C)  $( 7 , \infty )$ 
D)  $( - \infty , 1 )$ or $( 7 , \infty )$ 
A)  $( 1,7 )$ 
B)  $( - \infty , 1 )$ 
C)  $( 7 , \infty )$ 
D)  $( - \infty , 1 )$ or $( 7 , \infty )$

Question 6

Find the indicated intercept(s) of the graph of the function.
-$x$-intercepts of $f ( x ) = \frac { x ^ { 2 } + 9 x } { x ^ { 2 } + 7 x - 9 }$

Accepted Answer

A)  $( 0,0 ) , ( - 9,0 )$ 
B)  $( - 9,0 )$ 
C)  $( 9,0 )$ 
D)  $( 0,0 ) , ( 9,0 )$ 
A)  $( 0,0 ) , ( - 9,0 )$ 
B)  $( - 9,0 )$ 
C)  $( 9,0 )$ 
D)  $( 0,0 ) , ( 9,0 )$

Question 7

Find the x- and y-intercepts of f.
-$$f ( x ) = ( x + 13 ) ^ { 2 }$$

Accepted Answer

A)  $x$-intercept: $- 13$; y-intercept: 169 
B)  $x$-intercept: $- 13$; $y$-intercept: 0 
C)  $x$-intercept: 13; $y$-intercept: 169 
D)  x-intercept: 13 ; $y$-intercept: 0 
A)  $x$-intercept: $- 13$; y-intercept: 169 
B)  $x$-intercept: $- 13$; $y$-intercept: 0 
C)  $x$-intercept: 13; $y$-intercept: 169 
D)  x-intercept: 13 ; $y$-intercept: 0

Question 8

Find the indicated intercept(s) of the graph of the function.
-$y$-intercept of $f ( x ) = \frac { 23 } { ( x + 10 ) \left( x ^ { 2 } - 5 \right) }$

Accepted Answer

A)  $\left( 0 , \frac { 23 } { 50 } \right)$ 
B)  $\left( 0 , - \frac { 23 } { 50 } \right)$ 
C)  $( 0,23 )$ 
D)  none 
A)  $\left( 0 , \frac { 23 } { 50 } \right)$ 
B)  $\left( 0 , - \frac { 23 } { 50 } \right)$ 
C)  $( 0,23 )$ 
D)  none

Question 9

Give the equation of the oblique asymptote, if any, of the function.
-$$f ( x ) = \frac { x ^ { 2 } + 2 x - 6 } { x - 4 }$$

Accepted Answer

A)  no oblique asymptotes 
B)  $x = y + 6$ 
C)  $y = x + 6$ 
D)  $y = x - 2$ 
A)  no oblique asymptotes 
B)  $x = y + 6$ 
C)  $y = x + 6$ 
D)  $y = x - 2$

Question 10

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
-$$f ( x ) = - 15 x ^ { 4 } + \pi x ^ { 3 } + 1$$

Accepted Answer

A)  Yes; degree 8 
B)  Yes; degree 7 
C)  No; $x ^ { 3 }$ has a non-integer coefficient 
D)  Yes; degree 4 
A)  Yes; degree 8 
B)  Yes; degree 7 
C)  No; $x ^ { 3 }$ has a non-integer coefficient 
D)  Yes; degree 4

Question 11

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.
-$$f ( x ) = 2 \left( x ^ { 2 } + 1 \right) \left( x ^ { 2 } + 6 \right) ^ { 2 }$$

Accepted Answer

A)  No real zeros 
B)  $- 1$, multiplicity 1 , touches $x$-axis; $- 6$, multiplicity 2 , crosses $x$-axis 
C)  1 , multiplicity 1 , crosses $x$-axis; $- 1$, multiplicity 1 , crosses $x$-axis; 
$\sqrt { 6 }$, multiplicity 2 , touches $x$-axis; $- \sqrt { 6 }$, multiplicity 2 , touches $x$-axis 
D)  $- 1$, multiplicity 1 , crosses $x$-axis; $- 6$, multiplicity 2 , touches $x$-axis 
A)  No real zeros 
B)  $- 1$, multiplicity 1 , touches $x$-axis; $- 6$, multiplicity 2 , crosses $x$-axis 
C)  1 , multiplicity 1 , crosses $x$-axis; $- 1$, multiplicity 1 , crosses $x$-axis; 
$\sqrt { 6 }$, multiplicity 2 , touches $x$-axis; $- \sqrt { 6 }$, multiplicity 2 , touches $x$-axis 
D)  $- 1$, multiplicity 1 , crosses $x$-axis; $- 6$, multiplicity 2 , touches $x$-axis

Question 12

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.
-Zeros: $- 5$, multiplicity $2 ; - 1$, multiplicity 1 ; degree 3

Accepted Answer

A)  $x ^ { 3 } + 11 x ^ { 2 } + 35 x + 25$ 
B)  $x ^ { 3 } - 11 x ^ { 2 } + 10 x - 25$ 
C)  $x ^ { 3 } + 10 x ^ { 2 } + 35 x + 25$ 
D)  $x ^ { 3 } - 11 x ^ { 2 } + 35 x - 25$ 
A)  $x ^ { 3 } + 11 x ^ { 2 } + 35 x + 25$ 
B)  $x ^ { 3 } - 11 x ^ { 2 } + 10 x - 25$ 
C)  $x ^ { 3 } + 10 x ^ { 2 } + 35 x + 25$ 
D)  $x ^ { 3 } - 11 x ^ { 2 } + 35 x - 25$

Question 13

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.
-Zeros: 3, multiplicity $2 ; - 3$, multiplicity 2 ; degree 4

Accepted Answer

A)  $f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 18 x ^ { 2 } - 27 x + 81$ 
B)  $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } - 18 x ^ { 2 } + 27 x - 81$ 
C)  $f ( x ) = x ^ { 4 } + 18 x ^ { 2 } + 81$ 
D)  $f ( x ) = x ^ { 4 } - 18 x ^ { 2 } + 81$ 
A)  $f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 18 x ^ { 2 } - 27 x + 81$ 
B)  $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } - 18 x ^ { 2 } + 27 x - 81$ 
C)  $f ( x ) = x ^ { 4 } + 18 x ^ { 2 } + 81$ 
D)  $f ( x ) = x ^ { 4 } - 18 x ^ { 2 } + 81$

Question 14

Graph the function using transformations.
-$f(x)=\frac{2}{(3+x)^{2}}$

Accepted Answer

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

Find all zeros of the function and write the polynomial as a product of linear factors. - $f ( x ) = x ^ { 3 } + 11 x ^ { 2 } + 36 x + 26$

Choose the one alternative that best completes the statement or answers the question. Find the domain of the rational function. - $g ( x ) = \frac { x + 8 } { x ^ { 2 } - 49 x }$

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. - $f ( x ) = 4 x ^ { 3 } + 19 x ^ { 2 } - 8 x + 15$

Solve the inequality. - $36 \left( x ^ { 2 } - 1 \right) > 65 x$

Solve the inequality. - $x ^ { 2 } - 8 x + 7 > 0$

Find the indicated intercept(s) of the graph of the function. - $x$ -intercepts of $f ( x ) = \frac { x ^ { 2 } + 9 x } { x ^ { 2 } + 7 x - 9 }$

Find the x- and y-intercepts of f. - $f ( x ) = ( x + 13 ) ^ { 2 }$

Find the indicated intercept(s) of the graph of the function. - $y$ -intercept of $f ( x ) = \frac { 23 } { ( x + 10 ) \left( x ^ { 2 } - 5 \right) }$

Give the equation of the oblique asymptote, if any, of the function. - $f ( x ) = \frac { x ^ { 2 } + 2 x - 6 } { x - 4 }$

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = - 15 x ^ { 4 } + \pi x ^ { 3 } + 1$

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. - $f ( x ) = 2 \left( x ^ { 2 } + 1 \right) \left( x ^ { 2 } + 6 \right) ^ { 2 }$

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1. -Zeros: $- 5$ , multiplicity $2 ; - 1$ , multiplicity 1 ; degree 3

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1. -Zeros: 3, multiplicity $2 ; - 3$ , multiplicity 2 ; degree 4

Graph the function using transformations. - $f(x)=\frac{2}{(3+x)^{2}}$ $Graph the function using transformations. - f(x)=\frac{2}{(3+x)^{2}}$

Functions and Their Graphs

Linear and Quadratic 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 3: Polynomial and Rational Functions

Find all zeros of the function and write the polynomial as a product of linear factors. - f(x)=x3+11x2+36x+26f ( x ) = x ^ { 3 } + 11 x ^ { 2 } + 36 x + 26f(x)=x3+11x2+36x+26

Choose the one alternative that best completes the statement or answers the question. Find the domain of the rational function. - g(x)=x+8x2−49xg ( x ) = \frac { x + 8 } { x ^ { 2 } - 49 x }g(x)=x2−49xx+8​

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. - f(x)=4x3+19x2−8x+15f ( x ) = 4 x ^ { 3 } + 19 x ^ { 2 } - 8 x + 15f(x)=4x3+19x2−8x+15

Solve the inequality. - 36(x2−1)>65x36 \left( x ^ { 2 } - 1 \right) > 65 x36(x2−1)>65x

Solve the inequality. - x2−8x+7>0x ^ { 2 } - 8 x + 7 > 0x2−8x+7>0

Find the indicated intercept(s) of the graph of the function. - xxx -intercepts of f(x)=x2+9xx2+7x−9f ( x ) = \frac { x ^ { 2 } + 9 x } { x ^ { 2 } + 7 x - 9 }f(x)=x2+7x−9x2+9x​

Find the x- and y-intercepts of f. - f(x)=(x+13)2f ( x ) = ( x + 13 ) ^ { 2 }f(x)=(x+13)2

Find the indicated intercept(s) of the graph of the function. - yyy -intercept of f(x)=23(x+10)(x2−5)f ( x ) = \frac { 23 } { ( x + 10 ) \left( x ^ { 2 } - 5 \right) }f(x)=(x+10)(x2−5)23​

Give the equation of the oblique asymptote, if any, of the function. - f(x)=x2+2x−6x−4f ( x ) = \frac { x ^ { 2 } + 2 x - 6 } { x - 4 }f(x)=x−4x2+2x−6​

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - f(x)=−15x4+πx3+1f ( x ) = - 15 x ^ { 4 } + \pi x ^ { 3 } + 1f(x)=−15x4+πx3+1

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. - f(x)=2(x2+1)(x2+6)2f ( x ) = 2 \left( x ^ { 2 } + 1 \right) \left( x ^ { 2 } + 6 \right) ^ { 2 }f(x)=2(x2+1)(x2+6)2

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1. -Zeros: −5- 5−5 , multiplicity 2;−12 ; - 12;−1 , multiplicity 1 ; degree 3

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1. -Zeros: 3, multiplicity 2;−32 ; - 32;−3 , multiplicity 2 ; degree 4

Graph the function using transformations. - f(x)=2(3+x)2f(x)=\frac{2}{(3+x)^{2}}f(x)=(3+x)22​