20 algebra questions (multiple choice)
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3question_1_of_20.docx|
Question 1 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 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) = x4 - 9x2
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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. |
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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. |
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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. |
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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. |
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Question 3 of 20 |
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8 times a number subtracted from the squared of that number can be expressed as:
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A. P(x) = x + 7x. |
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B. P(x) = x2 - 8x. |
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C. P(x) = x - x. |
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Question 4 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 5 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; no holes |
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Question 6 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 7 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 8 of 20 |
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The perimeter of a rectangle is 80 feet. If the length of the rectangle is represented by x, its width can be expressed as:
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A. 80 + x. |
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B. 20 - x. |
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C. 40 + 4x. |
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D. 40 - x. |
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Question 9 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 10 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 11 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 12 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 13 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 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. 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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Question 16 of 20 |
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If f is a polynomial function of degree n, then the graph of f has at most __________ turning points.
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A. n - 3 |
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B. n - f |
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C. n - 1 |
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D. n + f |
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Question 17 of 20 |
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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 18 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 19 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) = x3 - x - 1; between 1 and 2
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A. f(1) = -1; f(2) = 5 |
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B. f(1) = -3; f(2) = 7 |
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C. f(1) = -1; f(2) = 3 |
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D. f(1) = 2; f(2) = 7 |
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Question 20 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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