Like f g is also one to one whereas f is always

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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 √ √m • Powers of Radicals: n xm = ( n x) √ n x x • Quotient Rule: n = √ , provided y = 0. ny y √ √ • If n is odd, n xn = x; if n is even, n xn = |x|. • Product Rule: √ n...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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