Question - 1
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
Question - 2
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 - 3
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.
Question - 4
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 - 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
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.
Question - 7
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 - 8
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 - 9
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
Question - 10
If f is a polynomial function of degree n, then the graph of f has at most __________ turning points.
A. n - 3
B. n - f
C. n - 1
D. n + f
Question - 11
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 - 12
9x2 - 6x + 1 < 0
A. (-∞, -3)
B. (-1, ∞)
C. [2, 4)
D. Ø
Question - 13
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 - 14
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 - 15
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 - 16
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 - 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
Question - 18
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
A. f(1) = -1; f(2) = 5
B. f(1) = -3; f(2) = 7
C. f(1) = -1; f(2) = 3
D. f(1) = 2; f(2) = 7
Question - 19
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 - 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
