Question 1 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 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) = 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 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
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 5 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 6 of 20
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). A. f(x) = (2x - 4) + 4 B. f(x) = 2(2x + 8) + 3 C. f(x) = 2(x - 5)2 + 3 D. f(x) = 2(x + 3)2 + 3 Question 7 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 Question 8 of 20
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 9 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 10 of 20
Find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x) = 2(x - 3)2 + 1 A. (3, 1) B. (7, 2) C. (6, 5) D. (2, 1) 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
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 13 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 14 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 15 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; holes at 4x Question 16 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 17 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 18 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 19 of 20
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 20 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