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

2024
Views:

45

Pages:

1
Author:

Alejandro Callahan

PAL Worksheet 7 1. Let g(x) = 2(x + 1)2 − 3. a. Graph y = g(x). Explain why g is not invertible. b. Let f (x) = 2(x + 1)2 − 3, x ≤ −1. (The function f is just the function g with a restricted domain.) Explain why f is invertible. c. What are the domain and range of f ? What are the domain and range of f −1 . Graph the function f and, using the reflection about the line y = x, also graph f −1 on the same axes. d. Using algebra, determine the rule for f −1 (x). (Your final answer should include any restrictions on the domain of f −1 .) 2. A farmer has 1500 feet of fencing and wants to fence off a rectangular field, where one side of the field will be along a straight river which will not require any fencing. If x represents the width of the field, write a function that gives the area A of the field as a function of x. x 3. For each quadratic function, first complete the square and locate the vertex of the graph. Then sketch the graph, labeling the exact value of the y-intercept and the x-intercept(s), if any. a. f (x) = x2 − x − 12 b. f (x) = 3x2 − 6x + 8 c. f (x) = −3x2 + 4x + 1 d. f (x) = 35 x2 − 6x e. f (x) = 21 x2 + x − 5 f. f (x) = 3x2 − 21 x + 1