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:

 

·

A. 80 + x.

·

B. 20 – x.

·

C. 40 + 4x.

·

D. 40 – x.

 

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

 

·

A. 5; -2

·

B. 7; -4

·

C. 2; -5

·

D. 1; -9

 

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

 

Find the domain of the following rational function. g(x) = 3×2/((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}

 

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.

 

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

 

·

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

 

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

 

·

A. y = 3x + 5.

·

B. y = 6x + 7.

·

C. y = 2x – 5.

·

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)

 

·

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

 

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

 

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

 

·

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

 

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 asymptotea

 

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)

 

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

 

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

 

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)

 

·

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

·

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.

·

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.

·

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

 

·

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.

 

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.

 

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)

 

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

 

·

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

 

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

Basic features
  • Free title page and bibliography
  • Unlimited revisions
  • Plagiarism-free guarantee
  • Money-back guarantee
  • 24/7 support
On-demand options
  • Writer’s samples
  • Part-by-part delivery
  • Overnight delivery
  • Copies of used sources
  • Expert Proofreading
Paper format
  • 275 words per page
  • 12 pt Arial/Times New Roman
  • Double line spacing
  • Any citation style (APA, MLA, Chicago/Turabian, Harvard)