Question 1

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
-$$f ( x ) = 1 + \frac { 7 } { x }$$

Accepted Answer

A)  Yes; degree 7 
B)  Yes; degree 0 
C)  Yes; degree 1 
D)  No; x is raised to a negative power 
A)  Yes; degree 7 
B)  Yes; degree 0 
C)  Yes; degree 1 
D)  No; x is raised to a negative power

Question 2

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval.
-$f ( x ) = 3 x ^ { 4 } - 5 x ^ { 3 } + 25 x ^ { 2 } - 45 x - 18$

Accepted Answer

A)  $f ( x ) = ( 3 x + 1 ) ( x - 2 ) ( x + 3 ) ( x - 3 )$ 
B)  $f ( x ) = ( 3 x + 1 ) ( x - 2 ) ( x + 3 i ) ( x - 3 i )$ 
C)  $f ( x ) = ( 3 x - 1 ) ( x + 2 ) ( x + 3 i ) ( x - 3 i )$ 
D)  $f ( x ) = ( 3 x - 1 ) ( x + 2 ) ( x + 3 ) ( x - 3 )$ 
A)  $f ( x ) = ( 3 x + 1 ) ( x - 2 ) ( x + 3 ) ( x - 3 )$ 
B)  $f ( x ) = ( 3 x + 1 ) ( x - 2 ) ( x + 3 i ) ( x - 3 i )$ 
C)  $f ( x ) = ( 3 x - 1 ) ( x + 2 ) ( x + 3 i ) ( x - 3 i )$ 
D)  $f ( x ) = ( 3 x - 1 ) ( x + 2 ) ( x + 3 ) ( x - 3 )$

Question 3

List the potential rational zeros of the polynomial function. Do not find the zeros.
-$$f ( x ) = - 4 x ^ { 4 } + 2 x ^ { 2 } - 3 x + 6$$

Accepted Answer

A)  $\pm \frac { 1 } { 6 } , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 3 } , \pm \frac { 2 } { 3 } , \pm \frac { 4 } { 3 } , \pm 1 , \pm 2 , \pm 4$ 
B)  $\pm \frac { 1 } { 4 } , \pm \frac { 1 } { 2 } , \pm \frac { 3 } { 4 } , \pm \frac { 3 } { 2 } , \pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6$ 
C)  $\pm \frac { 1 } { 4 } , \pm \frac { 1 } { 2 } , \pm \frac { 3 } { 4 } , \pm \frac { 3 } { 2 } , \pm 1 , \pm 2 , \pm 3 , \pm 6$ 
D)  $\pm \frac { 1 } { 4 } , \pm \frac { 1 } { 2 } , \pm \frac { 2 } { 3 } , \pm \frac { 3 } { 4 } , \pm \frac { 3 } { 2 } , \pm 1 , \pm 2 , \pm 3 , \pm 6$ 
A)  $\pm \frac { 1 } { 6 } , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 3 } , \pm \frac { 2 } { 3 } , \pm \frac { 4 } { 3 } , \pm 1 , \pm 2 , \pm 4$ 
B)  $\pm \frac { 1 } { 4 } , \pm \frac { 1 } { 2 } , \pm \frac { 3 } { 4 } , \pm \frac { 3 } { 2 } , \pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6$ 
C)  $\pm \frac { 1 } { 4 } , \pm \frac { 1 } { 2 } , \pm \frac { 3 } { 4 } , \pm \frac { 3 } { 2 } , \pm 1 , \pm 2 , \pm 3 , \pm 6$ 
D)  $\pm \frac { 1 } { 4 } , \pm \frac { 1 } { 2 } , \pm \frac { 2 } { 3 } , \pm \frac { 3 } { 4 } , \pm \frac { 3 } { 2 } , \pm 1 , \pm 2 , \pm 3 , \pm 6$

Question 4

Find the x- and y-intercepts of f.
-f(x) = (x - 2)2(x2 - 9)

Accepted Answer

A)  x-intercepts: -3, 2, 3; y-intercept: 36 
B)  x-intercepts: -2, -9; y-intercept: 18 
C)  x-intercepts: 2, 9; y-intercept: 18 
D)  x-intercepts: -3, 2, 3; y-intercept: -36 
A)  x-intercepts: -3, 2, 3; y-intercept: 36 
B)  x-intercepts: -2, -9; y-intercept: 18 
C)  x-intercepts: 2, 9; y-intercept: 18 
D)  x-intercepts: -3, 2, 3; y-intercept: -36

Question 5

Find the x- and y-intercepts of f.
-f(x) = (x + 1)(x - 4)(x - 1)2

Accepted Answer

A)  x-intercepts: -1, 1, -4; y-intercept: -4 
B)  x-intercepts: -1, 1, 4; y-intercept: 4 
C)  x-intercepts: -1, 1, 4; y-intercept: -4 
D)  x-intercepts: -1, 1, -4; y-intercept: 4 
A)  x-intercepts: -1, 1, -4; y-intercept: -4 
B)  x-intercepts: -1, 1, 4; y-intercept: 4 
C)  x-intercepts: -1, 1, 4; y-intercept: -4 
D)  x-intercepts: -1, 1, -4; y-intercept: 4

Question 6

The equation has a solution r in the interval indicated. Approximate this solution correct to two decimal places.
-x4 - x3 - 7x2 + 5x + 10 = 0; -3 ≤ r ≤-2

Accepted Answer

Question 7

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) = x(x - 9)

Accepted Answer

A)  Yes; degree 1 
B)  Yes; degree 2 
C)  Yes; degree 0 
D)  No; it is a product 
A)  Yes; degree 1 
B)  Yes; degree 2 
C)  Yes; degree 0 
D)  No; it is a product

Question 8

Solve the equation in the real number system.
-$2 x ^ { 4 } - 2 x ^ { 3 } + x ^ { 2 } - 5 x - 10 = 0$

Accepted Answer

A)  $\left\{ - \frac { \sqrt { 10 } } { 2 } , \frac { \sqrt { 10 } } { 2 } \right\}$ 
B)  $\{ 1 , - 2 \}$ 
C)  $\{ - 1,2 \}$ 
D)  $\left\{ - \frac { 5 } { 2 } , \frac { 5 } { 2 } \right\}$ 
A)  $\left\{ - \frac { \sqrt { 10 } } { 2 } , \frac { \sqrt { 10 } } { 2 } \right\}$ 
B)  $\{ 1 , - 2 \}$ 
C)  $\{ - 1,2 \}$ 
D)  $\left\{ - \frac { 5 } { 2 } , \frac { 5 } { 2 } \right\}$

Question 9

List the potential rational zeros of the polynomial function. Do not find the zeros.
-$$f ( x ) = - 2 x ^ { 3 } + 2 x ^ { 2 } - 3 x + 8$$

Accepted Answer

A)  $\pm \frac { 1 } { 8 } , \pm \frac { 1 } { 4 } , \pm \frac { 1 } { 2 } , \pm 1 , \pm 2 , \pm 4 , \pm 8$ 
B)  $\pm \frac { 1 } { 2 } , \pm 1 , \pm 2 , \pm 4$ 
C)  $\pm \frac { 1 } { 4 } , \pm \frac { 1 } { 2 } , \pm 1 , \pm 2 , \pm 4 , \pm 8$ 
D)  $\pm \frac { 1 } { 2 } , \pm 1 , \pm 2 , \pm 4 , \pm 8$ 
A)  $\pm \frac { 1 } { 8 } , \pm \frac { 1 } { 4 } , \pm \frac { 1 } { 2 } , \pm 1 , \pm 2 , \pm 4 , \pm 8$ 
B)  $\pm \frac { 1 } { 2 } , \pm 1 , \pm 2 , \pm 4$ 
C)  $\pm \frac { 1 } { 4 } , \pm \frac { 1 } { 2 } , \pm 1 , \pm 2 , \pm 4 , \pm 8$ 
D)  $\pm \frac { 1 } { 2 } , \pm 1 , \pm 2 , \pm 4 , \pm 8$

Question 10

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval.
-f(x) = 8x5 - 7x3 - 10x2 + 4; [-1, 0]

Accepted Answer

A)  f(-1) = -7 and f(0) = -4; no 
B)  f(-1) = -7 and f(0) = 4; yes 
C)  f(-1) = 7 and f(0) = 4; no 
D)  f(-1) = 7 and f(0) = -4; yes 
A)  f(-1) = -7 and f(0) = -4; no 
B)  f(-1) = -7 and f(0) = 4; yes 
C)  f(-1) = 7 and f(0) = 4; no 
D)  f(-1) = 7 and f(0) = -4; yes

Question 11

Determine the maximum number of turning points of f.
-f(x) = (x - 3)2(x + 5)2

Accepted Answer

A)  3 
B)  1 
C)  4 
D)  2 
A)  3 
B)  1 
C)  4 
D)  2

Question 12

Find the x- and y-intercepts of f.
-f(x) = -x2 (x + 7)(x2 + 1)

Accepted Answer

A)  x-intercepts: -7, 0; y-intercept: 0 
B)  x-intercepts: -7, -1, 0; y-intercept: 7 
C)  x-intercepts: -7, -1, 0, 1; y-intercept: 0 
D)  x-intercepts: -7, -1, 0; y-intercept: -7 
A)  x-intercepts: -7, 0; y-intercept: 0 
B)  x-intercepts: -7, -1, 0; y-intercept: 7 
C)  x-intercepts: -7, -1, 0, 1; y-intercept: 0 
D)  x-intercepts: -7, -1, 0; y-intercept: -7

Question 13

Find the x- and y-intercepts of f.
-f(x) = 6x - x3

Accepted Answer

A)  x-intercepts: 0, -6; y-intercept: 0 
B)  x-intercepts: 0, 6, -6; y-intercept: 0 
C)  x-intercepts: 0, 6, - 6; y-intercept: 6 
D)  x-intercepts: 0, -6; y-intercept: 6 
A)  x-intercepts: 0, -6; y-intercept: 0 
B)  x-intercepts: 0, 6, -6; y-intercept: 0 
C)  x-intercepts: 0, 6, - 6; y-intercept: 6 
D)  x-intercepts: 0, -6; y-intercept: 6

Question 14

Solve the equation in the real number system.
-$2 x ^ { 3 } - x ^ { 2 } + 2 x - 1 = 0$

Accepted Answer

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

Question 15

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

Accepted Answer

A)  x-intercepts: -1, 1, -2; y-intercept: 2 
B)  x-intercepts: -1, 1, 2; y-intercept: 2 
C)  x-intercepts: -1, 1, -2; y-intercept: -2 
D)  x-intercepts: -1, 1, 2; y-intercept: -2 
A)  x-intercepts: -1, 1, -2; y-intercept: 2 
B)  x-intercepts: -1, 1, 2; y-intercept: 2 
C)  x-intercepts: -1, 1, -2; y-intercept: -2 
D)  x-intercepts: -1, 1, 2; y-intercept: -2

Question 16

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) = 4x + 2x3

Accepted Answer

A)  Yes; degree 3 
B)  Yes; degree 2 
C)  Yes; degree 1 
D)  Yes; degree 4 
A)  Yes; degree 3 
B)  Yes; degree 2 
C)  Yes; degree 1 
D)  Yes; degree 4

Question 17

Determine the maximum number of turning points of f.
-$$f ( x ) = ( x - 4 ) ^ { 3 }$$

Accepted Answer

A)  above the $x$-axis: $( 4 , \infty )$
below the $x$-axis: $( - \infty , 4 )$ 
B)  above the $x$-axis: $( - \infty , 4 ) , ( 4 , \infty )$
below the $x$-axis: no intervals 
C)  above the x-axis: no intervals
below the $x$-axis: $( - \infty , 4 ) , ( 4 , \infty )$ 
D)  above the $x$-axis: $( - \infty , 4 )$
below the $x$-axis: $( 4 , \infty )$ 
A)  above the $x$-axis: $( 4 , \infty )$
below the $x$-axis: $( - \infty , 4 )$ 
B)  above the $x$-axis: $( - \infty , 4 ) , ( 4 , \infty )$
below the $x$-axis: no intervals 
C)  above the x-axis: no intervals
below the $x$-axis: $( - \infty , 4 ) , ( 4 , \infty )$ 
D)  above the $x$-axis: $( - \infty , 4 )$
below the $x$-axis: $( 4 , \infty )$

Question 18

Determine the maximum number of turning points of f.
-$$f ( x ) = \left( x + \frac { 1 } { 9 } \right) ^ { 4 } ( x - 4 ) ^ { 3 }$$

Accepted Answer

A)  above the $x$-axis: $( 4 , \infty )$
below the $x$-axis: $\left( - \infty , - \frac { 1 } { 9 } \right) , \left( - \frac { 1 } { 9 } , 4 \right)$ 
B)  above the $x$-axis: $\left( - \infty , - \frac { 1 } { 9 } \right) , \left( - \frac { 1 } { 9 } , 4 \right)$
below the $x$-axis: $( 4 , \infty )$ 
C)  above the $x$-axis: $\left( - \frac { 1 } { 9 } , 4 \right)$
below the $x$-axis: $\left( - \infty , - \frac { 1 } { 9 } \right) , ( 4 , \infty )$ 
D)  above the x-axis: $\left( - \infty , - \frac { 1 } { 9 } \right) , ( 4 , \infty )$
below the $x$-axis: $\left( - \frac { 1 } { 9 } , 4 \right)$ 
A)  above the $x$-axis: $( 4 , \infty )$
below the $x$-axis: $\left( - \infty , - \frac { 1 } { 9 } \right) , \left( - \frac { 1 } { 9 } , 4 \right)$ 
B)  above the $x$-axis: $\left( - \infty , - \frac { 1 } { 9 } \right) , \left( - \frac { 1 } { 9 } , 4 \right)$
below the $x$-axis: $( 4 , \infty )$ 
C)  above the $x$-axis: $\left( - \frac { 1 } { 9 } , 4 \right)$
below the $x$-axis: $\left( - \infty , - \frac { 1 } { 9 } \right) , ( 4 , \infty )$ 
D)  above the x-axis: $\left( - \infty , - \frac { 1 } { 9 } \right) , ( 4 , \infty )$
below the $x$-axis: $\left( - \frac { 1 } { 9 } , 4 \right)$

Question 19

Find the x- and y-intercepts of f.
-f(x) = -x2 (x + 2)(x2 - 1)

Accepted Answer

A)  x-intercepts: -2, 0, 1; y-intercept: -2 
B)  x-intercepts: -2, -1, 0, 1; y-intercept: -2 
C)  x-intercepts: -1, 0, 1, 2; y-intercept: 0 
D)  x-intercepts: -2, -1, 0, 1; y-intercept: 0 
A)  x-intercepts: -2, 0, 1; y-intercept: -2 
B)  x-intercepts: -2, -1, 0, 1; y-intercept: -2 
C)  x-intercepts: -1, 0, 1, 2; y-intercept: 0 
D)  x-intercepts: -2, -1, 0, 1; y-intercept: 0

Question 20

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

Accepted Answer

A)  No; it contains no variables 
B)  No; it is a constant 
C)  Yes; degree 1 
D)  Yes; degree 0 
A)  No; it contains no variables 
B)  No; it is a constant 
C)  Yes; degree 1 
D)  Yes; degree 0

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = 1 + \frac { 7 } { x }$

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. - $f ( x ) = 3 x ^ { 4 } - 5 x ^ { 3 } + 25 x ^ { 2 } - 45 x - 18$

List the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = - 4 x ^ { 4 } + 2 x ^ { 2 } - 3 x + 6$

Find the x- and y-intercepts of f. -f(x) = (x - 2)²(x² - 9)

Find the x- and y-intercepts of f. -f(x) = (x + 1)(x - 4)(x - 1)²

The equation has a solution r in the interval indicated. Approximate this solution correct to two decimal places. -x⁴ - x³ - 7x² + 5x + 10 = 0; -3 ≤ r ≤-2

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) = x(x - 9)

Solve the equation in the real number system. - $2 x ^ { 4 } - 2 x ^ { 3 } + x ^ { 2 } - 5 x - 10 = 0$

List the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = - 2 x ^ { 3 } + 2 x ^ { 2 } - 3 x + 8$

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. -f(x) = 8x⁵ - 7x³ - 10x² + 4; [-1, 0]

Determine the maximum number of turning points of f. -f(x) = (x - 3)²(x + 5)²

Find the x- and y-intercepts of f. -f(x) = -x² (x + 7)(x² + 1)

Find the x- and y-intercepts of f. -f(x) = 6x - x³

Solve the equation in the real number system. - $2 x ^ { 3 } - x ^ { 2 } + 2 x - 1 = 0$

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

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) = 4x + 2x³

Determine the maximum number of turning points of f. - $f ( x ) = ( x - 4 ) ^ { 3 }$

Determine the maximum number of turning points of f. - $f ( x ) = \left( x + \frac { 1 } { 9 } \right) ^ { 4 } ( x - 4 ) ^ { 3 }$

Find the x- and y-intercepts of f. -f(x) = -x² (x + 2)(x² - 1)

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

Functions and Their Graphs

Linear and Quadratic Functions

Conics

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

Filters

Exam 3: Polynomial and Rational Functions

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)=1+7xf ( x ) = 1 + \frac { 7 } { x }f(x)=1+x7​

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. - f(x)=3x4−5x3+25x2−45x−18f ( x ) = 3 x ^ { 4 } - 5 x ^ { 3 } + 25 x ^ { 2 } - 45 x - 18f(x)=3x4−5x3+25x2−45x−18

List the potential rational zeros of the polynomial function. Do not find the zeros. - f(x)=−4x4+2x2−3x+6f ( x ) = - 4 x ^ { 4 } + 2 x ^ { 2 } - 3 x + 6f(x)=−4x4+2x2−3x+6

Find the x- and y-intercepts of f. -f(x) = (x - 2)2(x2 - 9)

Find the x- and y-intercepts of f. -f(x) = (x + 1)(x - 4)(x - 1)2

The equation has a solution r in the interval indicated. Approximate this solution correct to two decimal places. -x4 - x3 - 7x2 + 5x + 10 = 0; -3 ≤ r ≤-2

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) = x(x - 9)

Solve the equation in the real number system. - 2x4−2x3+x2−5x−10=02 x ^ { 4 } - 2 x ^ { 3 } + x ^ { 2 } - 5 x - 10 = 02x4−2x3+x2−5x−10=0

List the potential rational zeros of the polynomial function. Do not find the zeros. - f(x)=−2x3+2x2−3x+8f ( x ) = - 2 x ^ { 3 } + 2 x ^ { 2 } - 3 x + 8f(x)=−2x3+2x2−3x+8

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. -f(x) = 8x5 - 7x3 - 10x2 + 4; [-1, 0]

Determine the maximum number of turning points of f. -f(x) = (x - 3)2(x + 5)2

Find the x- and y-intercepts of f. -f(x) = -x2 (x + 7)(x2 + 1)

Find the x- and y-intercepts of f. -f(x) = 6x - x3

Solve the equation in the real number system. - 2x3−x2+2x−1=02 x ^ { 3 } - x ^ { 2 } + 2 x - 1 = 02x3−x2+2x−1=0

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

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) = 4x + 2x3

Determine the maximum number of turning points of f. - f(x)=(x−4)3f ( x ) = ( x - 4 ) ^ { 3 }f(x)=(x−4)3

Determine the maximum number of turning points of f. - f(x)=(x+19)4(x−4)3f ( x ) = \left( x + \frac { 1 } { 9 } \right) ^ { 4 } ( x - 4 ) ^ { 3 }f(x)=(x+91​)4(x−4)3

Find the x- and y-intercepts of f. -f(x) = -x2 (x + 2)(x2 - 1)