Unformatted text preview: the vertical steepening near x = 0 and the horizontal ﬂattening as x → ∞. y= √ x y= √
4 x y= √
6 x The odd-indexed radical functions also follow a predictable trend - steepening near x = 0 and
ﬂattening as x → ±∞. In the exercises, you’ll have a chance to graph some basic radical functions
using the techniques presented in Section 1.8. y= √
3 x y= √
5 x y= √
7 x We have used all of the following properties at some point in the textbook for the case n = 2 (the
square root), but we list them here in generality for completeness.
1 Although we discussed imaginary numbers in Section 3.4, we restrict our attention to real numbers in this section.
See the epilogue on page 226 for more details. 312 Further Topics in Functions Theorem 5.6. Properties of Radicals: Let x and y be real numbers and m and n be natural
numbers. If n x, n y are real numbers, then
xy = n x n y
• Powers of Radicals: n xm = ( n x)
• Quotient Rule: n
= √ , provided y = 0.
• If n is odd, n xn = x; if n is even, n xn = |x|.
• Product Rule: √
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