College Algebra

MAC 1105 Chapter 5 Test 2020 OLS

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

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1. 1) Zeros: -1, 1, - 5; degree 3 1)

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept.

2) f(x) = x + 1 5

2 (x + 2)3 2)

Find the x- and y-intercepts of f. 3) f(x) = 6x - x3 3)

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|. (b) Find the x- and y-intercepts of the graph. (c) Determine whether the graph crosses or touches the x-axis at each x-intercept. (d) Graph f using a graphing utility. (e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places. (f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points. (g) Find the domain of f. Use the graph to find the range of f. (h) Use the graph to determine where f is increasing and where f is decreasing.

4) f(x) = (x + 3)(x - 3)2 4)

Find the domain of the rational function.

5) f(x) = x + 5

x2 - 49 5)

Find the vertical asymptotes of the rational function.

6) R(x) = -3x2

x2 + 5x - 14 6)

Give the equation of the horizontal asymptote, if any, of the function.

7) f(x) = 2x2 + 3 2x2 - 3

7)

Give the equation of the oblique asymptote, if any, of the function.

8) f(x) = x2 - 2x + 4

x + 6 8)

1

Graph the function.

9) f(x) = 2x

(x - 2)(x + 2) 9)

Solve the inequality. 10) (x + 7)(x + 1) > 0 10)

11) x2 - 9 0 11)

12) x - 1 x + 7

> 0 12)

Use the Remainder Theorem to find the remainder when f(x) is divided by x - c. 13) f(x) = x4 + 8x3 + 12x2; x + 1 13)

Use the Factor Theorem to determine whether x - c is a factor of f(x). 14) f(x) = 7x4 + 20x3 - 3x2 + x + 3; x + 3 14)

Solve the equation in the real number system. 15) x3 + 6x2 + 11x + 6 = 0 15)

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