Two Linear Functions 1: Let f and g be defined by f(x) = 9 x 4 x 8 g(x) = x + 2 1 x 5 Figure 1-4f a. The graphs of f and g are shown in Figure 1-4f. Plot these graphs on your grapher, making sure they agree with the figure. On the same screen, plot the graphs of y = f(g(x)) and y = g(f(x)). Sketch the graphs, showing the domains of each. You may use a copy of Figure 1-4f. b. Find f(g(3)). Show on your sketch from part a the two steps by which you can find this value directly from the graphs of f and g. c. Explain why f(g(6)) is undefined. Explain why f(g(1)) is undefined, even though g(1) is defined. d. Find an equation for f(g(x)) explicitly in terms of x. Simplify as much as possible. e. Find the domains of both f g and g f algebraically. Do they agree with your graphs in part a? f. Find the range of f g algebraically. Does it agree with your graph in part a? g. Find f(f(5)). Explain why g(g(5)) is undefined.

LIB – 120 – Introduction to Psychology Chapter 1: The Science of Psychology Vocabulary Behavioral Perspective: A research perspective whose major explanatory focus is how external environmental events condition observable behavior. (3) Biological Perspective: A research perspective whose major explanatory focus is how the brain, nervous system, and other physiological mechanisms produce behavior and mental processes. (2) Case Study: A descriptive method in which the researcher studies an individual in depth over an extended period of time. (9) Cognitive Perspective: A research perspective whose major explanatory focus is how the mental processes such as perception, memory, and pr