Chapter 5 Assessment - Polynomial and Rational Functions

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

f(x) = 3x + 4x²

• Yes; degree 4

• Yes; degree 1

• Yes; degree 2

• Yes; degree 3

Use transformations of the graph of y = or y = to graph the function.

f(x) = x⁴+ 4

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For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches

the x-axis at each x -intercept.

f(x) = 4(x + 7)(x - 5)²

• A) -7, multiplicity 1, crosses x-axis; 5, multiplicity 2, touches x-axis

• B) 7, multiplicity 1, touches x-axis; -5, multiplicity 2, crosses x-axis

• C) -7, multiplicity 1, touches x-axis; 5, multiplicity 2, crosses x-axis

• D) 7, multiplicity 1, crosses x-axis; -5, multiplicity 2, touches x-axis

Find the x- and y-intercepts of f.

f(x) = (x + 1)(x - 8)(x - 1)²

• A) x-intercepts: -1, 1, -8; y-intercept: 8

• B) x-intercepts: -1, 1, 8; y-intercept: -8

• C) x-intercepts: -1, 1, 8; y-intercept: 8

• D) x-intercepts: -1, 1, -8; y-intercept: -8

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis.

f(x) = (x + 2)³

• A) above the x-axis: (-∞, -2), (-2, ∞)

  below the x-axis: no intervals

• B) above the x-axis: (-∞, -2)

  below the x-axis: (-2, ∞)

• C) above the x-axis: no intervals

  below the x-axis: (-∞, -2), (-2, ∞)

• D) above the x-axis: (-2, ∞)

  below the x-axis: (-∞, -2)

Write the word or phrase that best completes each statement or answers the question.

Analyze the graph of the given function f as follows:

(a) Determine the end behavior: find the power function that the graph of f resembles for large values

of |x|.

(a2) Graph f using a graphing utility.

(b-c) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to

two decimal places.

(d-e) Use the graph to determine where f is increasing and where f is decreasing.

f(x) = (x + 3)(x - 3)²​ ​ (a)   ​ (b)   ​ (c)   ​ (d)   ​ (e)  

• Local minimum at (3,0)
• f is increasing on (-∞, -1.00) and (3, ∞)
• f is decreasing on (32.00, 3)
• Local maximum at (-1.00, 32.00)
• y = x4
• Local maximum at (-1.33, 1.19)
• Local minimum at (0,0)
• f is increasing in (-∞, -1.33)
• f is decreasing on (-1.33, 0)

• A) {x|x ≠ -7, x ≠ 7}

• B) {x|x ≠ -7, x ≠ 7, x ≠ -5}

• C) all real numbers

• D) {x|x ≠ 0, x ≠ 49}

Use the graph to determine the domain and range of the function.

• A) domain: {x|x ≠ 5}

  range: {y|y ≠ 4}

• B) domain: {x|x ≠ 5}

  range: {y|y ≠ -4}

• C) domain: {x|x ≠ -4}

  range: {y|y ≠ 5}

• D) domain: {x|x ≠ 4}

  range: {y|y ≠ 5}

• A) x = -1, x = 1, x = -8

• B) x = 1, x = -8

• C) x = 0, x = 1

• D) x = -1, x = 1

• A) y = 1

• B) y = 2

• C) y = 3

• D) no horizontal asymptotes