{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Stitz-Zeager_College_Algebra_e-book

# This creates a vertical scaling8 by a factor of 2 as

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online