This creates a vertical scaling8 by a factor of 2 as

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Unformatted text preview: .2. Let f (x) = x. Use the graph of f from Example 1.8.1 to graph the following functions below. Also, state their domains and ranges. √ −x √ 2. j (x) = 3 − x √ 3. m(x) = 3 − x 1. g (x) = Solution. √ 1. The mere sight of −x usually causes alarm, if not panic. When we discussed domains in Section 1.5, we clearly banished negatives from the radicals of even roots. However, we must remember that x is a variable, and as such, the quantity −x isn’t always negative. For √ example, if x = −4, −x = 4, thus −x = −(−4) = 2 is perfectly well-defined. To find the 1.8 Transformations 91 domain analytically, we set −x ≥ 0 which gives x ≤ 0, so that the domain of g is (−∞, 0]. Since g (x) = f (−x), Theorem 1.4 tells us the graph of g is the reflection of the graph of f across the y -axis. We can accomplish this by multiplying each x-coordinate on the graph of f by −1, so that the points (0, 0), (1, 1), and (4, 2) move to (0, 0), (−1, 1), and (−4, 2), respectively. Graphically, we see that the domain of g is (−∞, 0] and the range of g is the same a...
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