Chapter 5.1, Problem 55E

Decomposing Functions If f(x)=x2+3, express f as a composition of two functions.

Use a graphing utility to graph f(x)=10|x-|2 on the viewing window [0,4] . Identify the corresponding range. Show the graph.

The figure shows a contour graph of fas a function of x and y. contours f(x, y) y 10 5 1.0 0.5 -3 0 _2 0.5 -10 (a) Consider any point (x, y) on the graph. What happens to the function output when x remains constant and y increases? as y increases along any line perpendicular to the x-axis. The output of f ---Select--- (b) Consider the point (-1, 5). When x is decreased by 1/2, by what amount must y change for the point to remain on the same contour curve? In order for f(-1.5, y) to remain on the same contour curve as f(-1, 5), y must ---Select--- by (c) Consider the point (-2, -2). When y is increased by 1.5, by what amount must x change in order for the output to remain constant? In order for the output of f(x, -0.5) to remain constant with f(-2, -2), x must ---Select--- by