How to Find the Range of a FunctionDate: 02/25/98 at 16:44:12 From: Lynae Hunt Subject: How to find the range I'm a precalculus student at Elkhart Lake High School in Elkhart Lake, Wisconsin. My teacher and I are stumped on how to figure out the range for problems. An example of a problem is g(x) = (x+1)/(x^2-1). The book gives the range as (negative infinity, -1/2)U(-1/2, 0)U(0, infinity). My question to you is how they got that range? How did they get the -1/2? Thanks for the help Date: 02/26/98 at 09:38:17 From: Doctor Anthony Subject: Re: How to find the range The range represents the set of values that y can take. You must exclude values which are impossible or undefined. For example, if x = -1, y = 0/0. x+1 1 We could write y = ----------- = -----, provided x NOT equal to -1. (x+1)(x-1) x-1 1 However, ----- = -1/2, as x -> -1 -1-1 So y is tending to the value -1/2 but does not equal -1/2. When x -> 1 from below, y -> -infinity; and when x -> 1 from above, y -> +infinity. Finally, y = 0 is an asymptote, since the curve approaches y = 0 from below when x -> -infinity, and from above when x -> +infinity. So y can take all values from -infinity to +infinity, but we exclude y = -1/2, where the curve is not defined; and exclude y = 0, which is an asymptote. The statement you gave above for the range is simply expressing these facts. -Doctor Anthony, The Math Forum Check out our web site http://mathforum.org/dr.math/ |
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