Deck 4: Polynomial and Rational Functions

Question 1

Find the domain of the rational function f (x) = .

A) (-?, -2) ? (-2, ?)
B) [25, ?)
C) (-?, 2] ? [2, ?)
D) (-?, 2) ? (2, ?)

Answer 1

(-?, 2) ? (2, ?)

Question 2

Find the domain of the rational function.
F (x) =

A) (-?, -8) ? (8, ?)
B) (-?, -8) ? (-8, 5/4) ? (5/4, ?)
C) (-8, 5/4)
D) (-?, -3/5) ? (3/5, ?)

Answer 2

(-?, -8) ? (-8, 5/4) ? (5/4, ?)

Question 3

Find the domain of the rational function f (x) = .

A) (-?, 1/9) ? (1/9, ?)
B) (-?, 0) ? (0, 1/9) ? (1/9, ?)
C) (1/9, ?)
D) (-?, -5/7) ? (-5/7, ?)

Answer 3

(-?, 0) ? (0, 1/9) ? (1/9, ?)

Question 4

Find the domain of the function f (x) = .

A) (-?, 6) ? (9, ?)
B) (-?, -9) ? (-9, -6) ? (-6, ?)
C) (-?, 6) ? (6, 9) ? (6, ?)
D) (-?, 6] ? [6, 9] ? [6, ?)

Question 5

Find the domain of the function f (x) = .

A) (-5, 5)
B) (-?, -5) ? (-5, 5) ? (5, ?)
C) (-?, -5) ? (5, ?)
D) (-?, ?)

Question 6

For the rational function f (x) = , find all the vertical asymptotes and horizontal asymptotes.

A)
B)
C)
D)

Question 7

For the rational function f (x) = , find all vertical and horizontal asymptotes.

A) vertical asymptotes x = -1 and x = -7, horizontal asymptote y = 2
B) vertical asymptotes x = -1 and x = -7, horizontal asymptote y =
C) no vertical asymptotes, horizontal asymptote y = 2
D) vertical asymptotes x = 1 and x = 7, horizontal asymptote y =

Question 8

For the rational function f (x) = , find all vertical and horizontal asymptotes.

A) vertical asymptote at 5, there is no horizontal asymptote
B) vertical asymptote at -5, horizontal asymptote at 5
C) vertical asymptote at -5, there is no horizontal asymptote
D) vertical asymptote at 5, horizontal asymptote at -5

Question 9

Professor Ito is teaching a large lecture course and is trying to learn students' names. The number of names he can remember, N(t), increases with each week in the semester, t, and is given by the rational function:N(t) = How many students' names does Professor Ito know by the fourth week of the semester? How many students' names should he know by the end of the semester (16 weeks)? Round your answer to the nearest whole number.

Question 10

Use the graphing strategy to graph the rational function.

Question 11

Match the rational function to the graph.

A)

B)

C)

D)

Question 12

Match the graph to the rational function.

A)
B)
C)
D)

Question 13

For the given graph of the rational function determine: (a) all intercepts, (b) all asymptotes, and (c) equation of the rational function.

Question 14

For the given graph of the rational function determine: (a) all intercepts, (b) all asymptotes, and (c) equation of the rational function.

A)

B)

C)

D)

Question 15

For the rational function f (x) = , find the equation of the slant asymptote.

Question 16

For the rational function f (x) = , find the equation of the slant asymptote.

Question 17

Use the graphing strategy to graph the rational function.
f (x) =

Question 18

Use the graphing strategy to graph the rational function.
f (x) =

Question 19

Use the graphing strategy to graph the rational function.
f (x) =

Question 20

Find all zeros (real and complex). Factor the polynomial as a product of linear factors.

Question 21

Find all zeros (real and complex). Factor the polynomial as a product of linear factors.

Question 22

Find all zeros (real and complex). Factor the polynomial as a product of linear factors.

Question 23

Given a zero of the polynomial, determine all other zeros (real and complex) and write the polynomial in terms of a product of linear factors.

Question 24

Given a zero of the polynomial, determine all other zeros (real and complex) and write the polynomial in terms of a product of linear factors.

A) x = 2 - i, -2, 7;
P(x) = [x - (2 + i)][x - (2 - i)](x - 2)(x + 7)
B) x = 2 - i, -2, 7;
P(x) = [x - (2 + i)][x - (2 - i)](x + 2)(x - 7)
C) x = 2 - i, -2, 7;
P(x) = [x - (2 + i)][x - (2 - i)](x - 2)(x - 7)
D) x = 2 - i, -2, 7;
P(x) = [x - (2 + i)][x - (2 - i)](x + 2)(x + 7)

Question 25

Factor the polynomial as a product of linear factors.

Question 26

Factor the polynomial as a product of linear factors.

A) P(x) = [x + (-5 + 3i)][x + (-5 - 3i)](x - 5)(x + 4)
B) P(x) = [x - (-5 + 3i)][x - (-5 - 3i)](x + 5)(x + 4)
C) P(x) = [x - (-5 + 3i)][x - (-5 - 3i)](x - 5)(x - 4)
D) P(x) = [x - (-5 + 3i)][x - (-5 - 3i)](x - 5)(x + 4)

Question 27

Factor the polynomial as a product of linear factors.

Question 28

Factor the polynomial as a product of linear factors.

A) P(x) = [x + (2 - 3i)][x + (2 + 3i)](x - 1)
B) P(x) = [x - (2 - 3i)][x - (2 + 3i)](x + 1)
C) P(x) = [x - (2 - 3i)][x - (2 + 3i)](x - 1)
D) P(x) = [x - (-2 - 3i)][x + (-2 + 3i)](x + 1)

Question 29

Find a polynomial of minimum degree that has these zeros.

Question 30

Find a polynomial of minimum degree that has these zeros.

Question 31

Find a polynomial of minimum degree that has these zeros.

Question 32

For the polynomial f (x) = + 3 - 5x + 3, use synthetic division to find f (-3).

A) -18
B) -12
C) 18
D) 12

Question 33

For the polynomial function f (x) = 5 +3x - 7, use synthetic division to find f (6).

A) 1091
B) 1104
C) 1182
D) 6

Question 34

Determine whether the number 2 is a zero of f (x) = + 5 - 22x + 16. If it is, find the other real zeros.

A) 2 is not a zero.
B) 2 is a zero and the others are 1 and -8.
C) 2 is a zero and the others are -1 and 8.
D) 2 is a zero and there are no other real zeros.

Question 35

Determine whether the number -7 is a zero of f (x) = + 3 - 36x + 32. If it is, find the other real zeros.

A) -7 is not a zero.
B) -7 is a zero and the others are 3 and -36.
C) -7 is a zero and the other is 32.
D) -7 is a zero and there are no other real zeros.

Question 36

Determine whether -5 is a zero of the polynomial. If it is, then find the other real zeros.P(x) = + 4 - 4x + 5

A) -5 is not a zero.
B) -5 is a zero and the other zeros are 4 and -4.
C) -5 is a zero and the other is 5.
D) -5 is a zero and there are no other real zeros.

Question 37

Given that 4 is a zero of the polynomial P(x) = - 11 + 34x - 24, determine all other zeros.

A) -6 and 1
B) 6 and 1
C) -6 and -1
D) 6 and -1

Question 38

Use Descartes' rule of signs to determine the possible number of positive real zeros and negative real zeros.

A)
B)
C)
D)

Question 39

Use Descartes' rule of signs to determine the possible number of positive real zeros and negative real zeros.

A)
B)
C)
D)

Question 40

Use Descartes' rule of signs to determine the possible number of positive real zeros and negative real zeros.

A)
B)
C)
D)

Question 41

Use Descartes' rule of signs to determine the possible number of positive real zeros, negative real zeros, and imaginary zeros.

A)
B)
C)
D)

Question 42

Use the rational zero theorem to list the possible rational zeros of the polynomial

A) {±1/3, ±1/11, ±1/7, ±1/33, ±1/77, ±1/21, ±1/231}
B) {±1, ±3, ±11, ±7}
C) {±1, ±3, ±11, ±7, ±33, ±77, ±21, ±231}
D) {±1/3, ±1/11, ±1/7}

Question 43

Use the rational zero theorem to list the possible rational zeros.

A) {±1, ±3}
B) {±1}
C) {±1, ±1/7}
D) {±1, ±1/3}

Question 44

Use the rational zero theorem to list the possible rational zeros.

A) {±1, ±1/11, ±7/11}
B) {±1, ±11, ±7, ±77}
C) {±1, ±11, ±7, ±77, ±1/11, ±7/11}
D) {±1, ±11, ±7}

Question 45

Given that -4 is a zero of the polynomial P(x) = + 7 + 14x + 8, determine all other zeros and write the polynomial in terms of a product of linear factors.

Question 46

Use the rational zero theorem to list the possible rational zeros.

Question 47

Use the intermediate value theorem to approximate the real zero in the indicated interval. Approximate to two decimal places if necessary.r

Question 48

Use the rational zero theorem to list the possible rational zeros.P(x) = 4 - 8 + 11x - 55

Question 49

Use Descartes' rule of signs to determine the possible number of positive real zeros, negative real zeros, and imaginary zeros.P(x) = - 3 + 3x + 6

Question 50

Use Descartes' rule of signs along with the rational root theorem to sketch a graph of the polynomial.

Question 51

Use long division to divide the polynomials. Express the answers in the form of and

A) Q(x) = x + 2; r(x) = 10
B) Q(x) = x + 2; r(x) = 0
C) Q(x) = + 4x + 13; r(x) = 10
D) Q(x) = x + 2; r(x) = -10

Question 52

Use long division to divide

Question 53

Use long division to divide

Question 54

Compute the following using synthetic division.

Question 55

Divide the polynomials by either long division or synthetic division.

Question 56

Divide the polynomials.

Question 57

Divide the polynomials.

Question 58

Divide the polynomials by either long division or synthetic division.

Question 59

The area of a rectangle is . If the width of the rectangle is find the length.

Question 60

Determine if the function is a polynomial. If it is, state the degree.

A) Not a polynomial
B) a polynomial of degree 21
C) a polynomial of degree 42
D) a polynomial of degree 4

Question 61

Determine if the function f is a polynomial. If it is, state the degree.

A) Not a polynomial
B) a polynomial of degree 17
C) a polynomial of degree 39
D) a polynomial of degree -39

Question 62

Determine if the function is a polynomial. If it is, state the degree

A) Not a polynomial
B) a polynomial of degree 18
C) a polynomial of degree 7
D) a polynomial of degree 25

Question 63

Find all the real zeros (and state their multiplicity) of the polynomial function.

A) 0, -7, 1
B) -7, 1
C) 0 (multiplicity 4), -7, and 1
D) 0 (multiplicity 4), 7, and -1

Question 64

Find all the real zeros (and state their multiplicity) of the polynomial function.

A) 0, 1 (multiplicity 2)
B) 0, -1, (multiplicity 2)
C) 1, 1, (multiplicity 2), 20 (multiplicity 2)
D) 0, 1 (multiplicity 2),

Question 65

Find all the real zeros (and state their multiplicity) of the polynomial function.

A) 0, 8
B) 0 (multiplicity 4), 8 (multiplicity 2)
C) 8 (multiplicity 2)
D) 0 (multiplicity 6), 8 (multiplicity 2)

Question 66

Find a polynomial of minimum degree with zeros 4, -3 and 5 (of multiplicity 2).

A)
B)
C)
D)

Question 67

Find a polynomial of minimum degree that has zeros -9, 0 (multiplicity 2) and 7.

A)
B)
C)
D)

Question 68

Find a polynomial of minimum degree with zeros 0, 10 + , and 10 - .

A)
B)
C)
D)

Question 69

Find a polynomial of minimum degree that has the zeros (with multiplicity 2) and - (with multiplicity 2).

A)
B)
C)
D)

Question 70

For the polynomial function , determine whether the graph touches or crosses at the x - intercept (-16, 0).

A) crosses the y - axis at (-16, 0)
B) touches the y - axis at (-16, 0)
C) crosses the x - axis at (-16, 0)
D) touches the x - axis at (-16, 0)

Question 71

For the polynomial function , determine whether the graph touches or crosses at the x-intercept (0, 0).

A) touches the x-axis at (0, 0)
B) crosses the x-axis at (0, 0)
C) touches the x-axis at (14, 0)
D) neither

Question 72

For the polynomial function , find the y-intercept.

A) (1, 0)
B) (-1, 0)
C) (0, 0)
D) (0, 1)

Question 73

For the polynomial function , find the y-intercept.

A) (0, -48)
B) (0, -96)
C) (0, 48)
D) (0, 2)

Question 74

Determine if the function is a polynomial. If it is, state the degree.

Question 75

Find all the real zeros (and state their multiplicity) of the polynomial function.

Question 76

Find a polynomial of minimum degree that has the zeros (with multiplicity 2) and - (with multiplicity 2).

Question 77

Sketch the graph of the polynomial function.

Question 78

Sketch the graph of the polynomial function.

Question 79

Match the polynomial function with its graph.

A)

B)

C)

D)

Question 80

Match the polynomial function with its graph.

A)

B)

C)

D)