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

2024
Views:

415

Pages:

2
Author:

Asa Carrillo

PAL Worksheet 5 1. The following is the graph of a function f : 4 3 2 1 -4 -3 -2 1 -1 2 3 4 -1 -2 -3 -4 Graph each of the following functions: a. g(x) = f (x + 1) − 2. b. h(x) = 12 f (x) c. k(x) = f (2x) d. l(x) = f (−x) e. m(x) = −2f (x) 2. Let f (x) = 3x − 1 and g(x) = x2 − x + 1. Compute the values of (f ◦ g)(2), (g ◦ f )(2), (g ◦ g)(1) and (f ◦ f )(3). 3. Suppose that the graph of a function f contains the following three points: (−2, 4), (0, −2), and (2, 7). Find three points that are on the graphs of each of the following functions: a. g, where g is obtained from f by shifting right 3 units. b. h, where h is obtained from f by shifting down 4 units. c. k, where k is obtained from f by reflecting in the x-axis. d. l, where l is obtained from f by reflecting in the y-axis. e. m, where m is obtained from f by stretching away from the x-axis by a factor of 3. f. n, where n is obtained from f by compressing towards the x-axis by a factor of 3. g. p, where p is obtained from f by stretching away from the y-axis by a factor of 4. h. q, where q is obtained from f by compressing towards the y-axis by a factor of 4. 4. Let f (x) = 3x − 1 and g(x) = x2 − x + 1. Find formulas for (f ◦ g)(x) and (g ◦ f )(x). State the domain of f ◦ g and the domain of g ◦ f . x+1 2x + 3 and g(x) = . Answer each question. x−4 2x − 1 a. Is it possible to compute (f ◦ g)( 21 )? Explain. 5. Let f (x) = b. Is it possible to compute (f ◦ g)( 75 )? Explain. c. Is it possible to compute (f ◦ g)(4)? Explain. d. Is it possible to compute (g ◦ f )( 12 )? Explain. e. Is it possible to compute (g ◦ f )(− 10 3 )? Explain. 3 2x − 1 and g(x) = . Find formulas for (f ◦ g)(x) and (g ◦ f )(x). State the x−2 2x + 3 domain of f ◦ g and the domain of g ◦ f . 6. Let f (x) =