algebra 60 questions

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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

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5.0 Points

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)

3 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.

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

4 of 20

5.0 Points

"Y varies directly as the n^th power of x" can be modeled by the equation:

A. y = kxⁿ.
B. y = kx/n.
C. y = kx^*n.
D. y = kn^x.

5 of 20

5.0 Points

40 times a number added to the negative square of that number can be expressed as:

A(x) = x² + 20x.

B. A(x) = -x + 30x.

A(x) = -x² - 60x.

A(x) = -x² + 40x.

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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

Solve the following formula for the speciﬁed variable:

V = 1/3 lwh for h

7 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

8 of 20

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.
P(x) = x²+ 10x.

9of 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) = 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.

10 of 20

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

11 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

12 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]

13 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)

14 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) = -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

15 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}

16 of 20

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.

17 of 20

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.

18 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

19 of 20

Solve the following polynomial inequality.

9x² - 6x + 1 < 0

A. (-∞, -3)
B. (-1, ∞)
C. [2, 4)
D. Ø

20 of 20

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

1. Find the domain of following logarithmic function.

f(x) = ln (x - 2)²

A. (∞, 2) ∪ (-2, -∞)
B. (-∞, 2) ∪ (2, ∞)
C. (-∞, 1) ∪ (3, ∞)
D. (2, -∞) ∪ (2, ∞)

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What's This? I

2 . Solve the following exponential equation. Express the solution set in terms of natural logarithms or common logarithms to a decimal approximation, of two decimal places, for the solution.

e^x = 5.7

A. {ln 5.7}; ≈1.74
B. {ln 8.7}; ≈3.74
C. {ln 6.9}; ≈2.49
D. {ln 8.9}; ≈3.97

A. Log₄ 1/16 = 64
B. Log₂ 1/24 = -4
C. Log₂ 1/16 = -4
D. Log₄ 1/16 = 54

A. 10 grams after 10 seconds; 6 grams after 20 seconds
B. 12 grams after 10 seconds; 7 grams after 20 seconds
C. 4 grams after 10 seconds; 1 gram after 20 seconds
D. 8 grams after 10 seconds; 4 grams after 20 seconds

A. 2 log_yx + log_xy
B. 2 log_bx + log_by
C. log_x - log_by
D. log_bx – log_xy

A. A₀ = A₀e^kt; ln = e^kt; ln 2 = ln e^kt; ln 2 = kt; ln 2/k = t
B. 2A₀ = A₀e; 2= e^kt; ln = ln e^kt; ln 2 = kt; ln 2/k = t
C. 2A₀ = A₀e^kt; 2= e^kt; ln 2 = ln e^kt; ln 2 = kt; ln 2/k = t
D. 2A₀ = A₀e^kt; 2 = e^kt; ln 1 = ln e^kt; ln 2 = kt; ln 2/k = t^oe

A. 1/2 log_bx - 6 log_by + 3 log_bz
B. 1/2 log_b x - 9 log_b y - 3 log_b z
C. 1/2 log_b x + 3 log_b y + 6 log_b z
D. 1/2 log_b x + 3 log_b y - 3 log_b z

A. A = 20,000(1 + (0.06/4))^4t; A = 10,000(1 + (0.044/14))^12t
B. A = 15,000(1 + (0.07/4))^4t; A = 10,000(1 + (0.025/12))^12t
C. A = 10,000(1 + (0.05/4))^4t; A = 10,000(1 + (0.045/12))^12t
D. A = 25,000(1 + (0.05/4))^4t; A = 10,000(1 + (0.032/14))^12t

A. bx; (∞, -∞); (1, ∞)
B. bx; (-∞, -∞); (2, ∞)
C. bx; (-∞, ∞); (0, ∞)
D. bx; (-∞, -∞); (-1, ∞)

A. x² + x - 1/2(x + 1) + 4/2(x - 1)
B. x³ + x - 1/2(x + 1) + 3/2(x - 1)
C. x³ + x - 1/6(x - 2) + 3/2(x + 1)
D. x² + x - 1/2(x + 1) + 4/2(x - 1)

A. {(4, -3), (-1, 2)}
B. {(2, -3), (-1, 6)}
C. {(-4, -3), (-1, 3)}
D. {(2, -3), (-1, -2)}

A. z = 200x + 125y
B. z = 125x + 200y
C. z = 130x + 225y
D. z = -125x + 200y

A. 1/4
B. 3/5
C. 1/2
D. 2/7

A. 2 log₄ = 16
B. 2² = 4
C. 4⁴ = 256
D. 2⁴ = 16

A. {-3}
B. {-2}
C. {4}
D. {12}

A. log (xy)
B. log (xy³)
C. log (xy²)
D. log_y (xy)³

A. 50x + 150y > 2000
B. 100x + 150y > 1000
C. 70x + 250y > 2000
D. 55x + 150y > 3000

A. y = 2x² + x - 6
B. y = 2x² + 2x - 4
C. y = 2x² + 2x + 3
D. y = 2x² + x - 5

A. 1/3x + 1/x² - x + 5/4(x² + 4)
B. 1/5x + 1/x² - x + 4/4(x² + 6)
C. 1/4x + 1/x² - x + 4/4(x² + 4)
D. 1/3x + 1/x² - x + 3/4(x² + 5)

A. y = 2x² - x + 3
B. y = 2x² + x² + 9
C. y = 3x² - x - 4
D. y = 2x² + 2x + 4

A. {(1, 1/3, 0)}
B. {(1/4, 1/3, -2)}
C. {(1/3, 1/5, -1)}
D. {(1/2, 1/3, -1)}

A. 4/6(x - 2) - 8/7(4x + 1)
B. 4/7(x - 3) - 8/7(2x + 1)
C. 4/7(x - 2) - 8/7(3x + 1)
D. 4/6(x - 2) - 8/7(3x + 1)

A. {(5, 2), (-4, 1)}
B. {(4, 2), (3, 1)}
C. {(2, 2), (4, 1)}
D. {(6, 2), (7, 1)}

A. 1/4c/x - c - 1/2c/x + c
B. 1/2c/x - c - 1/2c/x + c
C. 1/3c/x - c - 1/2c/x + c
D. 1/2c/x - c - 1/3c/x + c

A. {(2, 2), (3, -2), (-1, 2), (-4, -2)}
B. {(7, 2), (3, -2), (-4, 2), (-3, -1)}
C. {(4, 2), (3, -2), (-5, 2), (-2, -2)}
D. {(3, 2), (3, -2), (-3, 2), (-3, -2)}

A. {(-6, -4), (2, 0)}
B. {(-4, -4), (1, 0)}
C. {(-3, -4), (2, 0)}
D. {(-5, -4), (3, 0)}

algebra 60 questions

Algebra

A. a/a – c +ac + b/(x – c)²
B. a/b – c +ac + b/(x – c)
C. a/a – b +ac + c/(x – c)²
D. a/a – b +ac + b/(x – c)