EXAMPLE 4Reflections

Graph (a) y = – √x (b) y = √-x.

Solution The starting point is the graph of f(x) = √x given in FIGURE 1.6.10(a).

(a)The graph of y = – √x is the reflection of the graph of f(x) = √x in the x-axis. Observe in FIGURE 1.6.10(b) that since (1, 1) is on the graph of f, the point (1, -1) is on the graph of y = – √x.

(b)The graph of y = √-x is the reflection of the graph of f(x) = √x in the y-axis. Observe in FIGURE 1.6.10(c) that since (1, 1) is on the graph of f, the point (–1, 1) is on the graph of y = √-x. The function y = √-x looks a little strange, but bear in mind that its domain is determined by the requirement that -x ≥ 0, or equivalently x ≤ 0, and so the reflected graph is defined on the interval (–∞, 0].

FIGURE 1.6.10 ...

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