Question

Use the horizontal line test to identify one-toone functions. 21. Use the horizontal line test to determine which of the following functions is a one-to-one function and therefore has an inverse. (A) $y=x^2+4 x+6$ (B) $y=|2 x|-1$ (C) $y=\frac{1}{x^2}$ (D) $y=3 x+8$ (E) $y=\sqrt{25-x^2}$

   Use the horizontal line test to identify one-toone functions.
21. Use the horizontal line test to determine which of the following functions is a one-to-one function and therefore has an inverse.
(A) $y=x^2+4 x+6$
(B) $y=|2 x|-1$
(C) $y=\frac{1}{x^2}$
(D) $y=3 x+8$
(E) $y=\sqrt{25-x^2}$
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Calculus for dummies: 1,001 calculus practice problems
Calculus for dummies: 1,001 calculus practice problems
Patrick Jones 1st Edition
Chapter 1, Problem 21 ↓
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Use the horizontal line test to identify one-toone functions. 21. Use the horizontal line test to determine which of the following functions is a one-to-one function and therefore has an inverse. (A) $y=x^2+4 x+6$ (B) $y=|2 x|-1$ (C) $y=\frac{1}{x^2}$ (D) $y=3 x+8$ (E) $y=\sqrt{25-x^2}$
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Transcript

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00:01 So they want us to use the horizontal line test to figure out which of these six functions from section 3 .2 are one to one.
00:10 So remember the horizontal line test is we draw a horizontal line like this, and it will be one to one if it only intersects the graph once.
00:21 So notice how for the absolute value of y, this is not one to one, since it intersects this horizontal line.
00:31 In two places.
00:32 We do the same thing over here for x squared, draw horizontal line, and then notice we intersect at two places...
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