Question 1 of 20
5.0 Points
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 2 of 20
5.0 Points
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 3 of 20
5.0 Points
The perimeter of a rectangle is 80 feet. If the length of the rectangle is represented by x, its width can be expressed as:
A. 80 + x.
B. 20 - x.
C. 40 + 4x.
D. 40 - x.
Question 4 of 20
5.0 Points
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 5 of 20
5.0 Points
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 6 of 20
5.0 Points
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 7 of 20
5.0 Points
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 8 of 20
5.0 Points
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 9 of 20
5.0 Points
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 10 of 20
5.0 Points
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 11 of 20
5.0 Points
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 12 of 20
5.0 Points
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 13 of 20
5.0 Points
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
Question 14 of 20
5.0 Points
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 15 of 20
5.0 Points
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 16 of 20
5.0 Points
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 17 of 20
5.0 Points
Solve the following polynomial inequality.
9x2 - 6x + 1 < 0
A. (-∞, -3)
B. (-1, ∞)
C. [2, 4)
D. Ø
Question 18 of 20
5.0 Points
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 19 of 20
5.0 Points
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 20 of 20
5.0 Points
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
