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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