Math 3

Qu esti on 1

5 points Sa ve

Find the indicated intercept(s) of the graph of the function.

x-intercepts of f(x) =

(9, 0) (-9, 0) (0, 0) and (-9, 0) (0, 0) and (9, 0)

Qu esti on 2

5 points Sa ve

Find all zeros of the function and write the polynomial as a product of linear factors.

f(x) = x4 + 6x3 + 17x2 + 54x + 72

f(x) = (x - 4)(x + 2)(x - 3)(x + 3) f(x) = (x + 4)(x + 2)(x - 3i)(x + 3i) f(x) = (x - 1)(x - 8)(x - 3i)(x + 3i)

f(x) = (x - i )(x + i )(x - 3)(x +3)

Qu esti on 3

5 points Sa ve

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

4(x - 1)12(x + 1)9

Yes; degree 48 Yes; degree 21 Yes; degree 4 Yes; degree 12

Qu esti on 3

5 points Sa ve

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

4(x - 1)12(x + 1)9

Yes; degree 48 Yes; degree 21 Yes; degree 4 Yes; degree 12

Qu esti on 4

5 points Sa ve

Find the x- and y-intercepts of f.

f(x) = (x + 2)(x - 3)(x + 3)

x-intercepts: -3, 3, 2; y-intercept: 18 x-intercepts: -2, -3, 3; y-intercept: 18 x-intercepts: -3, 3, 2; y-intercept: -18

x-intercepts: -2, -3, 3; y-intercept: -18�� Question 5�5 points �Save � �Give the equation of the ob

lique asymptote, if any, of the function.

f(x) =

y = x - 3 x = y - 3 y = x - 9

no oblique asymptotes

Qu esti on 6

5 points Sa ve

Find the indicated intercept(s) of the graph of the function.

y-intercept of f(x) =

(0, 3) (0, 4)

Qu esti on 7

5 points Sa ve

Determine where the function is increasing and where it is decreasing.

f(x) = -x2 - 4x + 5

increasing on (-∞, 9) decreasing on (9, ∞) increasing on (-2, ∞) decreasing on (-∞, -2) increasing on (-∞, -2) decreasing on (-2, ∞) increasing on (9, ∞) decreasing on (-∞, 9)

Qu esti on 8

5 points Sa ve

Use the graph to find the horizontal asymptote, if any, of the function.

y = 0 x = 2 y = 3 y = 0, y = 3

Qu esti on 9

5 points Sa ve

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) = 4(x - 1)3

- , multiplicity 4, touches x-axis; 1, multiplicity 3, crosses x-axis

, multiplicity 4, touches x-axis; -1, multiplicity 3, crosses x-axis

, multiplicity 4, crosses x-axis; -1, multiplicity 3, touches x-axis

- , multiplicity 4, crosses x-axis; 1, multiplicity 3, touches x-axis

Qu esti on 9

5 points Sa ve

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) = 4(x - 1)3

- , multiplicity 4, touches x-axis; 1, multiplicity 3, crosses x-axis

, multiplicity 4, touches x-axis; -1, multiplicity 3, crosses x-axis

, multiplicity 4, crosses x-axis; -1, multiplicity 3, touches x-axis

- , multiplicity 4, crosses x-axis; 1, multiplicity 3, touches x-axis

Qu esti on 10

5 points Sa ve

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis.

f(x) = (x - 2)2(x + 4)2

above the x-axis: (-4, 2) below the x-axis: (-∞, -4), (2, ∞) above the x-axis: no intervals below the x-axis: (-∞, -4), (-4, 2), (2, ∞) above the x-axis: (-∞, -4), (2, ∞) below the x-axis: (-4, 2) above the x-axis: (-∞, -4), (-4, 2), (2, ∞) below the x-axis: no intervals

Qu esti on 11

5 points Sa ve

Solve.

While traveling in a car, the centrifugal force a passenger experiences as the car drives in a circle varies jointly as the mass of the passenger and the square of the speed of the car. If the a passenger experiences a force of 162 newtons when the car is moving at a speed of 60 kilometers per hour and the passenger has a mass of 50 kilograms, find the force a passenger experiences when the car is moving at 40 kilometers per hour and the passenger has a mass of 100 kilograms.

128 newtons 144 newtons 160 newtons 176 newtons

Qu esti on 11

5 points Sa ve

Solve.

While traveling in a car, the centrifugal force a passenger experiences as the car drives in a circle varies jointly as the mass of the passenger and the square of the speed of the car. If the a passenger experiences a force of 162 newtons when the car is moving at a speed of 60 kilometers per hour and the passenger has a mass of 50 kilograms, find the force a passenger experiences when the car is moving at 40 kilometers per hour and the passenger has a mass of 100 kilograms.

128 newtons 144 newtons 160 newtons 176 newtons

Qu esti on 12

5 points Sa ve

Use the graph to find the vertical asymptotes, if any, of the function.

x = -3, x = 3, x = 0 x = -3, x = 3, y = 0 none x = -3, x = 3

Qu esti on 12

5 points Sa ve

Use the graph to find the vertical asymptotes, if any, of the function.

x = -3, x = 3, x = 0 x = -3, x = 3, y = 0 none x = -3, x = 3

Qu esti on 13

5 points Sa ve

Solve the equation in the real number system.

2x4 - 2x3 + x2 - 5x - 10 = 0

�{-1, 2}�������{1, -2}�����

Qu esti on 15

5 points Sa ve

Find the vertex and axis of symmetry of the graph of the function.

f(x) = -5x2 - 2x - 2

; x = -5

; x = (5, -2); x = 5

; x = -

Qu esti on 16

5 points Sa ve

Solve.

The power that a resistor must dissipate is jointly proportional to the square of the current flowing through the resistor and the resistance of the resistor. If a resistor needs to dissipate of power when

of current is flowing through the resistor whose resistance is find the power that a resistor needs to dissipate when

of current are flowing through a resistor whose resistance is

63 watts 147 watts 84 watts 21 watts

Qu esti on 17

5 points Sa ve

Find all zeros of the function and write the polynomial as a product of linear factors.

f(x) = x3 + 8x2 + 22x + 20

f(x) = (x + 2)(x + 3 + i)(x + 3 - i) f(x) = (x + 2)(x + 3 + i)(x - 3 - i)

f(x) = (x - 1)(x + 3 + i )(x + 3 - i )

f(x) = (x + 1)(x + 3 + i )(x - 2 - i )

Qu esti on 17

5 points Sa ve

Find all zeros of the function and write the polynomial as a product of linear factors.

f(x) = x3 + 8x2 + 22x + 20

f(x) = (x + 2)(x + 3 + i)(x + 3 - i) f(x) = (x + 2)(x + 3 + i)(x - 3 - i)

f(x) = (x - 1)(x + 3 + i )(x + 3 - i )

f(x) = (x + 1)(x + 3 + i )(x - 2 - i )

Qu esti on 18

5 points Sa ve

Solve the inequality.

(x + 1)(x - 3) ≤ 0

(-∞, -1] [-1, 3] [3, ∞) (-∞, -1] or [3, ∞)

Qu esti on 19

5 points Sa ve

Solve the inequality.

≥ 0

(-∞, -7) or [-2, 6) or [12, ∞) (-∞, -7) or [12, ∞) (-7, -2] or (6, 12] (-∞, -7) or [-2, 0) or (0, 6) or [12, ∞)

Qu esti on 19

5 points Sa ve

Solve the inequality.

≥ 0

(-∞, -7) or [-2, 6) or [12, ∞) (-∞, -7) or [12, ∞) (-7, -2] or (6, 12] (-∞, -7) or [-2, 0) or (0, 6) or [12, ∞)

Qu esti on 20

5 points Sa ve

Form a polynomial whose zeros and degree are given.

Zeros: -1, 1, - 2; degree 3

f(x) = x3 - 2x2 + x - 2 for a = 1

f(x) = x3 - 2x2 - x + 2 for a = 1

f(x) = x3 + 2x2 + x + 2 for a = 1

f(x) = x3 + 2x2 - x - 2 for a = 1