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 xintercepts. State whether the graph crosses the xaxis, or touches the xaxis 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 xaxis at 2 and 3; f(x) touches the xaxis at 1


B. x = 6, x = 3, x = 2 ; f(x) crosses the xaxis at 6 and 3; f(x) touches the xaxis at 2.


C. x = 7, x = 2, x = 0 ; f(x) crosses the xaxis at 7 and 2; f(x) touches the xaxis at 0.


D. x = 2, x = 0, x = 1 ; f(x) crosses the xaxis at 2 and 1; f(x) touches the xaxis 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

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


