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Question 1 of 20 Find the x-intercepts

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Question 1 of 20

Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.

 

f(x) = -2x⁴ + 4x³

 

A. x = 1, x = 0; f(x) touches the x-axis at 1 and 0

               

B. x = -1, x = 3; f(x) crosses the x-axis at -1 and 3

               

C. x = 0, x = 2; f(x) crosses the x-axis at 0 and 2

               

D. x = 4, x = -3; f(x) crosses the x-axis at 4 and -3

 

 

Question 2 of 20

Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.

 f(x) = x³ + 2x² - x - 2

 

A. x = 2, x = 2, x = -1; f(x) touches the x-axis at each.

               

B. x = -2, x = 2, x = -5; f(x) crosses the x-axis at each.

               

C. x = -3, x = -4, x = 1; f(x) touches the x-axis at each.

               

D. x = -2, x = 1, x = -1; f(x) crosses the x-axis at each.

 

 

Question 3 of 20

"Y varies directly as the nth power of x" can be modeled by the equation:

 

A. y = kxⁿ.

               

B. y = kx/n.

               

C. y = kx*n.

               

D. y = knx.

 

 

Question 4 of 20

Find the domain of the following rational function.

f(x) = 5x/x – 4

 

A. {x ?x ≠ 3}

               

B. {x ?x = 5}

               

C. {x ?x = 2}

               

D. {x ?x ≠ 4}

 

 

Question 5 of 20

Write an equation that expresses each relationship. Then solve the equation for y.

x varies jointly as y and z

 

A. x = kz; y = x/k

               

B. x = kyz; y = x/kz

               

C. x = kzy; y = x/z

               

D. x = ky/z; y = x/zk

 

 

Question 6 of 20

Solve the following polynomial inequality.

3x2 + 10x - 8 ≤ 0

 

A. [6, 1/3]

               

B. [-4, 2/3]

               

C. [-9, 4/5]

               

D. [8, 2/7]

 

 

 

 

Question 7 of 20

The perimeter of a rectangle is 80 feet. If the length of the rectangle is represented by x, its width can be expressed as:

 

A. 80 + x.

               

B. 20 - x.

               

C. 40 + 4x.

               

D. 40 - x.

 

 

 

Question 8 of 20

Find the coordinates of the vertex for the parabola defined by the given quadratic function.

f(x) = -2(x + 1)2 + 5

 

A. (-1, 5)

               

B. (2, 10)

               

C. (1, 10)

               

D. (-3, 7)

 

 

 

Question 9 of 20

Determine the degree and the leading coefficient of the polynomial function f(x) = -2x³ (x - 1)(x + 5).

 

A. 5; -2

               

B. 7; -4

               

C. 2; -5

               

D. 1; -9

 

 

 

Question 10 of 20

Based on the synthetic division shown, the equation of the slant asymptote of f(x) = (3x2 - 7x + 5)/x – 4 is:

 

A. y = 3x + 5.

               

B. y = 6x + 7.

               

C. y = 2x - 5.

               

D. y = 3x2 + 7.

 

 

 

Question 11 of 20

Solve the following polynomial inequality.

9x2 - 6x + 1 < 0

 

A. (-∞, -3)

               

B. (-1, ∞)

               

C. [2, 4)

               

D. Ø

 

 

 

Question 12 of 20

The difference between two numbers is 8. If one number is represented by x, the other number can be expressed as:

 

A. x - 5.

               

B. x + 4.

               

C. x - 8.

               

D. x - x.

 

Question 13 of 20

Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of the following rational function.

f(x) = x/ x + 4

 

A. Vertical asymptote: x = -4; no holes

               

B. Vertical asymptote: x = -4; holes at 3x

               

C. Vertical asymptote: x = -4; holes at 2x

               

D. Vertical asymptote: x = -4; no holes

 

Question 14 of 20

Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 3x2 or g(x) = -3x2, but with the given maximum or minimum.

Minimum = 0 at x = 11

 

A. f(x) = 6(x - 9)

               

B. f(x) = 3(x - 11)²

               

C. f(x) = 4(x + 10)

               

D. f(x) = 3(x2 - 15)2

 

 

Question 15 of 20

Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers.

f(x) = 2x⁴ - 4x² + 1; between -1 and 0

 

A. f(-1) = -0; f(0) = 2

               

B. f(-1) = -1; f(0) = 1

               

C. f(-1) = -2; f(0) = 0

               

D. f(-1) = -5; f(0) = -3

 

 

Question 16 of 20

Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 3x2 or g(x) = -3x2, but with the given maximum or minimum.

Maximum = 4 at x = -2

 

A. f(x) = 4(x + 6)2 - 4

               

B. f(x) = -5(x + 8)2 + 1

               

C. f(x) = 3(x + 7)2 - 7

               

D. f(x) = -3(x + 2)2 + 4

 

 

Question 17 of 20

Find the domain of the following rational function.

 

f(x) = x + 7/ x2 + 49

A. All real numbers < 69

               

B. All real numbers > 210

               

C. All real numbers ≤ 77

               

D. All real numbers

 

 

 

 

Question 18 of 20

Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of the following rational function.

g(x) = x + 3/x(x + 4)

 

A. Vertical asymptotes: x = 4, x = 0; holes at 3x

               

B. Vertical asymptotes: x = -8, x = 0; holes at x + 4

               

C. Vertical asymptotes: x = -4, x = 0; no holes

               

D. Vertical asymptotes: x = 5, x = 0; holes at x – 3

 

 

Question 19 of 20

Find the domain of the following rational function.

g(x) = 3x2/((x - 5)(x + 4))

 

A. {x? x ≠ 3, x ≠ 4}

               

B. {x? x ≠ 4, x ≠ -4}

               

C. {x? x ≠ 5, x ≠ -4}

               

D. {x? x ≠ -3, x ≠ 4}

 

 

Question 20 of 20

All rational functions can be expressed as f(x) = p(x)/q(x), where p and q are __________ functions and q(x) ≠ 0.

 

A. horizontal asymptotes

               

B. polynomial

               

C. vertical asymptotes

               

D. slant asymptotes