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Find the domain of the following rational function.
g(x) = 3x2/((x - 5)(x + 4))
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A. {x? x ≠ 3, x ≠ 4}
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B. {x? x ≠ 4, x ≠ -4}
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C. {x? x ≠ 5, x ≠ -4}
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D. {x? x ≠ -3, x ≠ 4}
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Question 2 of 20
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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)
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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
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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.
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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.
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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.
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Question 3 of 20
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"Y varies directly as the nth power of x" can be modeled by the equation:
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A. y = kxn.
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B. y = kx/n.
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C. y = kx*n.
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D. y = knx.
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Question 4 of 20
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The graph of f(x) = -x3 __________ to the left and __________ to the right.
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A. rises; falls
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B. falls; falls
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C. falls; rises
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D. falls; falls
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Question 5 of 20
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Find the domain of the following rational function.
f(x) = 5x/x – 4
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A. {x ?x ≠ 3}
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B. {x ?x = 5}
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C. {x ?x = 2}
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D. {x ?x ≠ 4}
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Question 6 of 20
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Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 2x2, but with the given point as the vertex (5, 3).
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A. f(x) = (2x - 4) + 4
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B. f(x) = 2(2x + 8) + 3
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C. f(x) = 2(x - 5)2 + 3
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D. f(x) = 2(x + 3)2 + 3
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Question 7 of 20
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All rational functions can be expressed as f(x) = p(x)/q(x), where p and q are __________ functions and q(x) ≠ 0.
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A. horizontal asymptotes
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B. polynomial
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C. vertical asymptotes
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D. slant asymptotes
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Question 8 of 20
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The graph of f(x) = -x2 __________ to the left and __________ to the right.
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A. falls; rises
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B. rises; rises
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C. falls; falls
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D. rises; rises
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Question 9 of 20
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Find the coordinates of the vertex for the parabola defined by the given quadratic function.
f(x) = -2(x + 1)2 + 5
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A. (-1, 5)
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B. (2, 10)
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C. (1, 10)
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D. (-3, 7)
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Question 10 of 20
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Find the coordinates of the vertex for the parabola defined by the given quadratic function.
f(x) = 2(x - 3)2 + 1
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Solve the following polynomial inequality.
9x2 - 6x + 1 < 0
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A. (-∞, -3)
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B. (-1, ∞)
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C. [2, 4)
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D. Ø
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Question 12 of 20
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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
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A. f(-1) = -0; f(0) = 2
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B. f(-1) = -1; f(0) = 1
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C. f(-1) = -2; f(0) = 0
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D. f(-1) = -5; f(0) = -3
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Question 13 of 20
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Determine the degree and the leading coefficient of the polynomial function f(x) = -2x3 (x - 1)(x + 5).
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A. 5; -2
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B. 7; -4
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C. 2; -5
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D. 1; -9
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Question 14 of 20
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Write an equation that expresses each relationship. Then solve the equation for y.
x varies jointly as y and z
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A. x = kz; y = x/k
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B. x = kyz; y = x/kz
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C. x = kzy; y = x/z
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D. x = ky/z; y = x/zk
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Question 15 of 20
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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
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A. Vertical asymptote: x = -4; no holes
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B. Vertical asymptote: x = -4; holes at 3x
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C. Vertical asymptote: x = -4; holes at 2x
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D. Vertical asymptote: x = -4; holes at 4x
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Question 16 of 20
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Solve the following polynomial inequality.
3x2 + 10x - 8 ≤ 0
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A. [6, 1/3]
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B. [-4, 2/3]
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C. [-9, 4/5]
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D. [8, 2/7]
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Question 17 of 20
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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
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A. f(x) = 6(x - 9)
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B. f(x) = 3(x - 11)2
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C. f(x) = 4(x + 10)
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D. f(x) = 3(x2 - 15)2
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Question 18 of 20
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The difference between two numbers is 8. If one number is represented by x, the other number can be expressed as:
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A. x - 5.
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B. x + 4.
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C. x - 8.
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D. x - x.
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Question 19 of 20
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40 times a number added to the negative square of that number can be expressed as:
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A.
A(x) = x2 + 20x.
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B. A(x) = -x + 30x.
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C.
A(x) = -x2 - 60x.
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D.
A(x) = -x2 + 40x.
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Question 20 of 20
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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)
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A. Vertical asymptotes: x = 4, x = 0; holes at 3x
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B. Vertical asymptotes: x = -8, x = 0; holes at x + 4
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C. Vertical asymptotes: x = -4, x = 0; no holes
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D. Vertical asymptotes: x = 5, x = 0; holes at x - 3
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