Question: 1. 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
2. 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
3. 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
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.
5. 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
6. 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
7. 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.
8. Solve the following polynomial inequality.
9x2 - 6x + 1 < 0
A. (-∞, -3)
B. (-1, ∞)
C. [2, 4)
D. Ø
9. 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.
10. 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
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.
11. 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
12. 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.
13. 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}
14. 8 times a number subtracted from the squared of that number can be expressed as:
A. P(x) = x + 7x.
B. P(x) = x2 - 8x.
C. P(x) = x - x.
D. P(x) = x2 + 10x.
15. 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.
16. 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)
17. 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
18. 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
19. 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]
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)