Open the “Vertical Compressions and Stretches” interactive figure, which is available in the Video & Resource Library of MyLab Math (under Interactive Figures) or at bit.ly/3raFUGB.
(a) Use the drop-down menu to select the absolute value (|x|) function. The basic function f (x) = |x| is drawn in a dashed-blue line with three key points labeled. Set the slider labeled a to 1. Now, use the slider labeled a to slowly increase the value of a from 1 to 3. As you do this, notice the form of the function g(x) = af (x) and the behavior of the graph of the function g( x) = af (x) shown in green. Repeat this for other functions available in the drop-down menu. Based on what you observe, conclude when the right side of a function y = f (x) is multiplied by a positive number a > 1, the graph of the new function is obtained by multiplying each y-coordinate on the graph of y = f (x) by _______. The new graph is a________ (horizontally/vertically)________ (stretched/compressed) version of the graph of y = f (x).

(b) Use the drop-down menu to select the absolute value (x) function. The basic function f ( x) = x is drawn in a dashed-blue line with three key points labeled. Set the slider labeled a to 1. Now, use the slider labeled a to slowly decrease the value of a from 1 to 0.2. As you do this, notice the form of the function g(x) = af (x) and  the behavior of the graph of the function g(x) = af ( x) shown in green. Repeat this for other functions available in the drop-down menu. Based on what you observe, conclude when the right side of a function y = f (x) is multiplied by a positive number 0 < a < 1, the graph of the new function is obtained by multiplying each y-coordinate on the graph of y = f (x) by _______. The new graph is a_______ (horizontally/vertically)______(stretched/compressed) version of the graph of y = f (x).

(c) If y = f (x) is some function whose graph contains the point (2, 4), the graph of y = 3f ( x) would contain the point _______. Express your answer as an ordered pair.

(d) If y = f (x) is some function whose graph contains the point (5, 12), the graph of y = 1/3 f (x) would contain the point ________. Express your answer as an ordered pair.