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

2024
Views:

114

Pages:

2
Author:

Victor Vaughn

PAL Worksheet 9 1. A rectangular box with a square base and no top is to made from 48 square feet of material. If x represents the length of one edge of the square base, write the volume V of the box as a function of x. y x x 2. One of the following graphs is the graph of f (x) = −5(x + 3)2 (x + 1)3 (x − 2)2 (x − 3). Which is it? Give reasons to support your answer. I. -4 II. -3 -2 -1 1 2 3 4 -4 III. -4 -3 -3 -2 -1 1 2 3 4 -2 -1 1 2 3 4 IV. -2 -1 1 2 3 4 -4 -3 3. In each case, if possible, find a single polynomial function whose graph has all three of the given characteristics. (You may leave your answer in factored form.) If it is not possible to find such a polynomial, state this fact. a. • Crosses the x-axis at −4 and 3. • Touches, but does not cross, the x-axis at −1 and 2. • Has degree 8. b. • Crosses the x-axis at −4 and 2. • Touches, but does not cross, the x-axis at −1 . • Has degree 6. c. • Never touches the x-axis. • Has y-intercept −8. • Has degree 7. d. • Crosses the x-axis at −4, −2, and 3, and does not even touch the x-axis anywhere else. • Has degree 7. • Whenever x < −4, f (x) > 0.