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

2024
Views:

251

Pages:

1
Author:

Jace Trevino

PAL Worksheet 4 1. If the point (−3, 7) is on the graph of an equation, what other point(s) must be on the graph if the graph is symmetric about . . . a. the x-axis. b. the y-axis. c. the origin. d. both the x- and y-axis. 2. The graph of a function f contains the point (2, −5). a. The graph of a function g is obtained by shifting the graph of f 3 units to the right, then 2 units upward, then reflecting in the y-axis. Find a point on the graph of g. b. The graph of a function h is obtained by shifting the graph of f 4 units to the left, then 6 units downward, then reflecting in the x-axis. Find a point on the graph of h. 3. Find the function g that is finally graphed after the following three transformations are applied to the graph of f (x) = |x|. • Shift left 3 units. • Shift up 5 units. • Reflect about the y-axis. 4. Consider the graph of f (x) = x2 . Explain why compressing the graph of f horizontally toward the y-axis by a factor of 3 gives the same result as stretching the graph vertically away from the x-axis by a factor of 9. 5. Let f (x) = 3x2 + 4x. In each case, a function g is given whose graph can be obtained from the graph of f by performing a single transformation (that is, a shift left, right, up or down, a reflection in either the x-axis or y-axis, a stretch or compression by some factor away from or toward either the x-axis or y-axis). Describe the transformation that will transform the graph of f into the graph of g. a. g(x) = 3x2 − 4x b. g(x) = 3x2 + 4x − 2 c. g(x) = 6x2 + 8x d. g(x) = 27x2 + 12x e. g(x) = 34 x2 + 2x f. g(x) = −3x2 − 4x g. g(x) = 3(x − 1)2 + 4(x − 1)