Question 1 40 times a number added to the negative square of that number can be expressed as:

A. A(x) = x2 + 20x.

B. A(x) = -x + 30x.

C. A(x) = -x2 – 60x.

D. A(x) = -x2 + 40x.

Question 2 Solve the following polynomial inequality. 9×2 – 6x + 1 < 0

A. (-∞, -3)

B. (-1, ∞)

C. [2, 4)

D. Ø

Question 3

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 4 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) = x2(x – 1)3(x + 2)

A. x = -1, x = 2, x = 3 ; f(x) crosses the x-axis at 2 and 3; f(x) touches the x-axis at -1

B. x = -6, x = 3, x = 2 ; f(x) crosses the x-axis at -6 and 3; f(x) touches the x-axis at 2.

C. x = 7, x = 2, x = 0 ; f(x) crosses the x-axis at 7 and 2; f(x) touches the x-axis at 0.

D. x = -2, x = 0, x = 1 ; f(x) crosses the x-axis at -2 and 1; f(x) touches the x-axis at 0.

Question 5 “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 6 The graph of f(x) = -x2 __________ to the left and __________ to the right.

A. falls; rises

B. rises; rises

C. falls; falls

D. rises; rises

Question 7 The graph of f(x) = -x3 __________ to the left and __________ to the right.

A. rises; falls

B. falls; falls

C. falls; rises

D. falls; falls

Question 8 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) = x4 – 9×2

A. x = 0, x = 3, x = -3; f(x) crosses the x-axis at -3 and 3; f(x) touches the x-axis at 0.

B. x = 1, x = 2, x = 3; f(x) crosses the x-axis at 2 and 3; f(x) crosses the x-axis at 0.

C. x = 0, x = -3, x = 5; f(x) touches the x-axis at -3 and 5; f(x) touches the x-axis at 0.

D. x = 1, x = 2, x = -4; f(x) crosses the x-axis at 2 and -4; f(x) touches the x-axis at 0.

Question 9 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 10 The difference between two numbers is 8. If one number is XXXXX by x, the other number can be expressed as:

A. x – 5.

B. x + 4.

C. x – 8.

D. x – x.

Question 11 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 12 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 + 2×2 – 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 13 Find the domain of the following rational function. f(x) = x + 7/x2 + 49

A. All real numbers 210

C. All real numbers ≤ 77

D. All real numbers

Question 14 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 15 5.0 Points Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x) = 2×4 – 4×2 + 1; between -1 and 0

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

B. f(-1) = -1; f(0) = 1 Hence, there is one zero between x = -1 and x=1

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

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

Question 16 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) = -2×4 + 4×3

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

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