# Algebra Exam 3

The perimeter of a rectangle is 80 feet. If the length of the rectangle is represented by x, its width can be expressed as:

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A. 80 + x.

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B. 20 – x.

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C. 40 + 4x.

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D. 40 – x.

Determine the degree and the leading coefficient of the polynomial function f(x) = -2×3 (x – 1)(x + 5).

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A. 5; -2

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B. 7; -4

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C. 2; -5

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D. 1; -9

If f is a polynomial function of degree n, then the graph of f has at most __________ turning points.

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A. n – 3

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B. n – f

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C. n – 1

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D. n + f

Find the domain of the following rational function. g(x) = 3×2/((x – 5)(x + 4))

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A. {x│ x ≠ 3, x ≠ 4}

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B. {x│ x ≠ 4, x ≠ -4}

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C. {x│ x ≠ 5, x ≠ -4}

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D. {x│ x ≠ -3, x ≠ 4}

8 times a number subtracted from the squared of that number can be expressed as:

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A. P(x) = x + 7x.

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B.

P(x) = x2 – 8x.

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C. P(x) = x – x.

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D.

P(x) = x2+ 10x.

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) = -2×4 + 4×3

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A. x = 1, x = 0; f(x) touches the x-axis at 1 and 0

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B. x = -1, x = 3; f(x) crosses the x-axis at -1 and 3

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C. x = 0, x = 2; f(x) crosses the x-axis at 0 and 2

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D. x = 4, x = -3; f(x) crosses the x-axis at 4 and -3

Based on the synthetic division shown, the equation of the slant asymptote of f(x) = (3×2 – 7x + 5)/x – 4 is:

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A. y = 3x + 5.

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B. y = 6x + 7.

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C. y = 2x – 5.

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D. y = 3×2 + 7.

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)

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A. Vertical asymptotes: x = 4, x = 0; holes at 3x

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B. Vertical asymptotes: x = -8, x = 0; holes at x + 4

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C. Vertical asymptotes: x = -4, x = 0; no holes

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D. Vertical asymptotes: x = 5, x = 0; holes at x – 3

The graph of f(x) = -x2 __________ to the left and __________ to the right.

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A. falls; rises

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B. rises; rises

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C. falls; falls

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D. rises; rises

Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 3x2or g(x) = -3×2, but with the given maximum or minimum. Minimum = 0 at x = 11

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A. f(x) = 6(x – 9)

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B. f(x) = 3(x – 11)2

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C. f(x) = 4(x + 10)

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D. f(x) = 3(x2 – 15)2

All rational functions can be expressed as f(x) = p(x)/q(x), where p and q are __________ functions and q(x) ≠ 0.

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A. horizontal asymptotes

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B. polynomial

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C. vertical asymptotes

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D. slant asymptotea

Find the coordinates of the vertex for the parabola defined by the given quadratic function.  f(x) = -2(x + 1)2 + 5

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A. (-1, 5)

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B. (2, 10)

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C. (1, 10)

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D. (-3, 7)

Write an equation that expresses each relationship. Then solve the equation for y.  x varies jointly as y and z

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A. x = kz; y = x/k

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B. x = kyz; y = x/kz

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C. x = kzy; y = x/z

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D. x = ky/z; y = x/zk

Find the domain of the following rational function.   f(x) = x + 7/x2 + 49

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A. All real numbers < 69

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B. All real numbers > 210

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C. All real numbers ≤ 77

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D. All real numbers

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)

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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

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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.

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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.

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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.

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 – 9×2

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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.

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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.

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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.

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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.

The difference between two numbers is 8. If one number is represented by x, the other number can be expressed as:

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A. x – 5.

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B. x + 4.

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C. x – 8.

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D. x – x.

Find the coordinates of the vertex for the parabola defined by the given quadratic function.  f(x) = 2(x – 3)2 + 1

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A. (3, 1)

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B. (7, 2)

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C. (6, 5)

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D. (2, 1)

Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 3x2or g(x) = -3×2, but with the given maximum or minimum.  Maximum = 4 at x = -2

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A. f(x) = 4(x + 6)2 – 4

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B. f(x) = -5(x + 8)2 + 1

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C. f(x) = 3(x + 7)2 – 7

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D. f(x) = -3(x + 2)2 + 4

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

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A. f(1) = -1; f(2) = 5

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B. f(1) = -3; f(2) = 7

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C. f(1) = -1; f(2) = 3

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D. f(1) = 2; f(2) = 7

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