Let's look at an example of finding horizontal asymptotes: Find the horizontal asymptote of the following function: y=x+2x2+1\small{ \boldsymbol{\color{green}{y = \dfrac{x + 2}{x^2 + 1} }}}y=x2+1x+2 First, notice that the denominator is a sum of squares, so it doesn...
Step 3:Find any horizontal asymptotes by examining the end behavior of the graph. A horizontal asymptote is a horizontal liney=dthat the graph of the function approaches asxgets really large or really small. Step 4:Determine the domain by looking at the graph fr...
AP Calculus AB Skills Practice Jump to a specific example Andrew Noble View bio Steps for How to Differentiate Vertical Asymptotes from Discontinuities Step 1: Factor the numerator and denominator if necessary. Step 2: For the denominator, identify the values of {eq}x {/eq} that make...
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For the range we find what y values are included in the function. Since the only horizontal asymptote is y=2; y cannot be exactly 2; and we identified that y can continue to -∞ and ∞ then the range is (-∞,2)υ(2,∞).
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For graphing functions, we need to take care of domain, range, asymptotes, and holes. Also, we need to know at least two to three points on each part of the curve for graphing the function.
These asymptotes appear at x equals one half pi, at x equals one and a half pi, and so on. This happens because on one side of the asymptote the graph is approaching positive infinity and on the other side it’s approaching negative infinity, and it can’t be both! Another way to ...
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