Question 1

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval.
-$$f ( x ) = 7 x ^ { 3 } - 2 x + 2 ; [ - 1,0 ]$$

Accepted Answer

A)  $f ( - 1 ) = 3$ and $f ( 0 ) = - 2$; yes 
B)  $f ( - 1 ) = 3$ and $f ( 0 ) = 2$; no 
C)  $f ( - 1 ) = - 3$ and $f ( 0 ) = 2$; yes 
D)  $f ( - 1 ) = - 3$ and $f ( 0 ) = - 2$; no 
A)  $f ( - 1 ) = 3$ and $f ( 0 ) = - 2$; yes 
B)  $f ( - 1 ) = 3$ and $f ( 0 ) = 2$; no 
C)  $f ( - 1 ) = - 3$ and $f ( 0 ) = 2$; yes 
D)  $f ( - 1 ) = - 3$ and $f ( 0 ) = - 2$; no

Question 2

Find the domain of the rational function.
-$$R ( x ) = \frac { - 3 x ^ { 2 } } { x ^ { 2 } + 2 x - 35 }$$

Accepted Answer

A)  $\{ x | x \neq - 7,5 \rangle$ 
B)  $\{ x | x \neq 7,5 \rangle$ 
C)  $\{ x | x \neq - 35,1 \rangle$ 
D)  $\{ x | x \neq 7 , - 5 \rangle$ 
A)  $\{ x | x \neq - 7,5 \rangle$ 
B)  $\{ x | x \neq 7,5 \rangle$ 
C)  $\{ x | x \neq - 35,1 \rangle$ 
D)  $\{ x | x \neq 7 , - 5 \rangle$

Question 3

Find the power function that the graph of f resembles for large values of $| \mathbf { x } |$
-$$f ( x ) = ( x - 3 ) ^ { 3 }$$

Accepted Answer

A)  $y = x ^ { - 3 }$ 
B)  $y = x ^ { 3 }$ 
C)  $y = x ^ { 9 }$ 
D)  $y = x ^ { - 27 }$ 
A)  $y = x ^ { - 3 }$ 
B)  $y = x ^ { 3 }$ 
C)  $y = x ^ { 9 }$ 
D)  $y = x ^ { - 27 }$

Question 4

Find the domain of the rational function.
-$$g ( x ) = \frac { x } { x ^ { 3 } - 216 }$$

Accepted Answer

A)  $\{ x \mid x \neq 6 \}$ 
B)  $\{ x \mid x \neq 36 \}$ 
C)  $\{ x \mid x \neq - 6 \}$ 
D)  $\{ x \mid x \neq - 6,6 \}$ 
A)  $\{ x \mid x \neq 6 \}$ 
B)  $\{ x \mid x \neq 36 \}$ 
C)  $\{ x \mid x \neq - 6 \}$ 
D)  $\{ x \mid x \neq - 6,6 \}$

Question 5

Solve the problem.
-$$( x + 2 ) ( x - 7 ) \leq 0$$

Accepted Answer

A)  $( - \infty , - 2 ]$ or $[ 7 , \infty )$ 
B)  $[ - 2,7 ]$ 
C)  $( - \infty , - 2 ]$ 
D)  $[ 7 , \infty )$ 
A)  $( - \infty , - 2 ]$ or $[ 7 , \infty )$ 
B)  $[ - 2,7 ]$ 
C)  $( - \infty , - 2 ]$ 
D)  $[ 7 , \infty )$

Question 6

Find the x- and y-intercepts of f.
-$f ( x ) = ( x + 1 ) ( x - 6 ) ( x - 1 ) ^ { 2 }$

Accepted Answer

A)  x-intercepts: -1, 1, 6; y-intercept: 6 
B)  x-intercepts: -1, 1, 6; y-intercept: -6 
C)  x-intercepts: -1, 1, -6; y-intercept: -6 
D)  x-intercepts: -1, 1, -6; y-intercept: 6 
A)  x-intercepts: -1, 1, 6; y-intercept: 6 
B)  x-intercepts: -1, 1, 6; y-intercept: -6 
C)  x-intercepts: -1, 1, -6; y-intercept: -6 
D)  x-intercepts: -1, 1, -6; y-intercept: 6

Question 7

Solve the equation in the real number system.
-$3 x ^ { 3 } - 14 x ^ { 2 } + 13 x + 6 = 0$

Accepted Answer

A)  $\{ - 1 , - 1 , - 2 \}$ 
B)  $\left\{ \frac { 1 } { 3 } , 2 , - 3 \right\}$ 
C)  $\left\{ - \frac { 1 } { 3 } , 2,3 \right\}$ 
D)  $\{ 1 , - 1,2 \rangle$ 
A)  $\{ - 1 , - 1 , - 2 \}$ 
B)  $\left\{ \frac { 1 } { 3 } , 2 , - 3 \right\}$ 
C)  $\left\{ - \frac { 1 } { 3 } , 2,3 \right\}$ 
D)  $\{ 1 , - 1,2 \rangle$

Question 8

Give the maximum number of zeros the polynomial function may have. Use Descarte's Rule of Signs to determine how
many positive and how many negative zeros it may have.
-$f ( x ) = x ^ { 7 } + x ^ { 6 } + x ^ { 2 } + x + 8$

Accepted Answer

A)  7; 0 positive zeros; 1 negative zero 
B)  7; 0 positive zeros; 2 or 0 negative zeros 
C)  7; 0 positive zeros; 3 or 1 negative zeros 
D)  7; 0 positive zeros; 0 negative zeros 
A)  7; 0 positive zeros; 1 negative zero 
B)  7; 0 positive zeros; 2 or 0 negative zeros 
C)  7; 0 positive zeros; 3 or 1 negative zeros 
D)  7; 0 positive zeros; 0 negative zeros

Question 9

Find the vertical asymptotes of the rational function.
-$$f ( x ) = \frac { - x ^ { 2 } + 16 } { x ^ { 2 } + 5 x + 4 }$$

Accepted Answer

A)  $x = 1 , x = - 4$ 
B)  $x = - 1 , x = - 4$ 
C)  $x = - 1$ 
D)  $x = - 1 , x = 4$ 
A)  $x = 1 , x = - 4$ 
B)  $x = - 1 , x = - 4$ 
C)  $x = - 1$ 
D)  $x = - 1 , x = 4$

Question 10

Give the equation of the horizontal asymptote, if any, of the function.
-$$f ( x ) = \frac { 3 x ^ { 2 } + 4 } { 3 x ^ { 2 } - 4 }$$

Accepted Answer

A)  $y = 4$ 
B)  $y = 3$ 
C)  $y = 1$ 
D)  no horizontal asymptotes 
A)  $y = 4$ 
B)  $y = 3$ 
C)  $y = 1$ 
D)  no horizontal asymptotes

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. - $f ( x ) = 7 x ^ { 3 } - 2 x + 2 ; [ - 1,0 ]$

Find the domain of the rational function. - $R ( x ) = \frac { - 3 x ^ { 2 } } { x ^ { 2 } + 2 x - 35 }$

Find the power function that the graph of f resembles for large values of $| \mathbf { x } |$ - $f ( x ) = ( x - 3 ) ^ { 3 }$

Find the domain of the rational function. - $g ( x ) = \frac { x } { x ^ { 3 } - 216 }$

Solve the problem. - $( x + 2 ) ( x - 7 ) \leq 0$

Find the x- and y-intercepts of f. - $f ( x ) = ( x + 1 ) ( x - 6 ) ( x - 1 ) ^ { 2 }$

Solve the equation in the real number system. - $3 x ^ { 3 } - 14 x ^ { 2 } + 13 x + 6 = 0$

Give the maximum number of zeros the polynomial function may have. Use Descarte's Rule of Signs to determine how many positive and how many negative zeros it may have. - $f ( x ) = x ^ { 7 } + x ^ { 6 } + x ^ { 2 } + x + 8$

Find the vertical asymptotes of the rational function. - $f ( x ) = \frac { - x ^ { 2 } + 16 } { x ^ { 2 } + 5 x + 4 }$

Give the equation of the horizontal asymptote, if any, of the function. - $f ( x ) = \frac { 3 x ^ { 2 } + 4 } { 3 x ^ { 2 } - 4 }$

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

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Exam 3: Polynomial and Rational Functions

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. - f(x)=7x3−2x+2;[−1,0]f ( x ) = 7 x ^ { 3 } - 2 x + 2 ; [ - 1,0 ]f(x)=7x3−2x+2;[−1,0]

Find the domain of the rational function. - R(x)=−3x2x2+2x−35R ( x ) = \frac { - 3 x ^ { 2 } } { x ^ { 2 } + 2 x - 35 }R(x)=x2+2x−35−3x2​

Find the power function that the graph of f resembles for large values of ∣x∣| \mathbf { x } |∣x∣ - f(x)=(x−3)3f ( x ) = ( x - 3 ) ^ { 3 }f(x)=(x−3)3

Find the domain of the rational function. - g(x)=xx3−216g ( x ) = \frac { x } { x ^ { 3 } - 216 }g(x)=x3−216x​

Solve the problem. - (x+2)(x−7)≤0( x + 2 ) ( x - 7 ) \leq 0(x+2)(x−7)≤0

Find the x- and y-intercepts of f. - f(x)=(x+1)(x−6)(x−1)2f ( x ) = ( x + 1 ) ( x - 6 ) ( x - 1 ) ^ { 2 }f(x)=(x+1)(x−6)(x−1)2

Solve the equation in the real number system. - 3x3−14x2+13x+6=03 x ^ { 3 } - 14 x ^ { 2 } + 13 x + 6 = 03x3−14x2+13x+6=0

Give the maximum number of zeros the polynomial function may have. Use Descarte's Rule of Signs to determine how many positive and how many negative zeros it may have. - f(x)=x7+x6+x2+x+8f ( x ) = x ^ { 7 } + x ^ { 6 } + x ^ { 2 } + x + 8f(x)=x7+x6+x2+x+8

Find the vertical asymptotes of the rational function. - f(x)=−x2+16x2+5x+4f ( x ) = \frac { - x ^ { 2 } + 16 } { x ^ { 2 } + 5 x + 4 }f(x)=x2+5x+4−x2+16​

Give the equation of the horizontal asymptote, if any, of the function. - f(x)=3x2+43x2−4f ( x ) = \frac { 3 x ^ { 2 } + 4 } { 3 x ^ { 2 } - 4 }f(x)=3x2−43x2+4​