1) Shifts and relfectdions: Let f (x) := x’. Then do the following graph f(x) and f(x+2) in the same coordinate system (carefully choose x and y range) • write a comment about what relates the two graphs. graph f(x) and f(x) – 3 in the same coordinate system (carefully choose x and y range) • write a comment about what relates the two graphs. graph f(x) and f(-x) in the same coordinate system (carefully choose x and y range) • write a comment about what relates the two graphs. graph f(x) and -f(x) in the same coordinate system (carefully choose x and y range) • write a comment about what relates the two graphs. graph f(x) and -f(-x) in the same coordinate system (carefully choose x and y range) • write a comment about what relates the two graphs. Now try to shift the graph of the function other ways. For example shift it to the right by 3, shift it to the left by 4, shift it up by 5, and shift it down by 6. 2) Define the absolute value function g(x) := abs(x). Repeat some of the steps from problem 1

Suppose a, b, c, and d are integers, and that a is negative and odd, b is positive and even, c is positive and odd, and d is positive and odd. For each of the six functions (a) – (f) choose one of the graphs I- XIE. - corresponds to graph. corresponds to graph (a) y = -e corresponds to graph, (b) y (c) y = -az° corresponds to graph, (d) y = (e) y = corresponds to graph, (f) y = cz" corresponds to graph . _ IV V VI VII VII IX XI II Figure 0.1

2. Sketch the graph of following functions -1 x(x - 5) a) y = b) y -3 (x+3)²

Consider the graph of f(x). y 10 -10 -5 10 -5 -10- 3.