University:
University of Vermont
Course:
MATH 1034 | Pre-Calculus Mathematics
Academic year:

2024
Views:

449

Pages:

2
Author:

Shelby Rollins

PAL Worksheet 8 1. If possible, write the function f (x) = 2x2 − x − 2 in the form f (x) = a(x − r1 )(x − r2 ) where a, r1 and r2 are real numbers. If it is not possible to write f in this form, explain how you know. 2. Let f (x) = −27(x + 4)5 (x + 2)2 (x − 1)(x − 3)3 (x2 + 3x + 5). a. What is the degree of f ? b. Is f (2) positive, negative, or zero? c. Write a power function (in the form g(x) = axn ) where the graph of f and the graph of g have the same end behavior. 3. The following graph is that of the function f (x) = x4 + 3x3 − 9x2 − 23x − 12. Using the graph, guess the factorization of f . Check your answer by multiplying out your guess. 250 200 150 100 50 -5 -4 -3 -2 1 -1 -50 2 3 4 5 4. The graph of a polynomial function y = f (x) is shown. 4 2 1 -7 -6 -5 -4 -3 -2 -1 2 3 4 5 6 7 -2 -4 Answer each question. a. Is the degree of f even or odd? b. Is the leading coefficient positive or negative? c. What is the smallest possible degree of f ? 5. The graph of a polynomial function y = g(x) is shown. 15 10 5 -6 -5 -4 -3 -2 1 -1 2 3 -5 -10 Answer each question. a. Is the degree of g even or odd? b. Is the leading coefficient positive or negative? c. What is the smallest possible degree of g? 4 5 6