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Using your calculator, determine the vertical asymptote of the function defined in Example 11.

Algebra

Chapter 1

Functions and their Applications

Section 7

More on Functions

Functions

Missouri State University

McMaster University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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Use tne graph to answer th…

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Find the horizontal asympt…

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Use a graphing calculator …

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Asymptotes Use analytical …

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Use analytical methods and…

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Find the vertical asymptot…

for a problem. 42 were given the equation of a rational function and were asked to determine the equation of any horizontal Assam totes if they're already so horizontal. Lesson twits are generally have a rational function, are determined by the highest degree term off the numerator and the denominator, so we don't actually care about any subsequent terms. We're just looking at the highest degree term off the numerator and the denominator. So I'm just gonna look at X to the 1/2 X squared and then anything else on the top. There isn't anything else, but anything else is just kind of superfluous. RN behavior. So it's X gets infinitely large in the positive or negative direction. We want to know what happens to our vertical value. What happens toe? Why are output and all these subsequent terms? So anything that's added really becomes unimportant as excuse infinitely large. And so we just look at those Those leading terms is leading coefficients, and we're really only concerned at this point with the degree on those coefficient. So we have a degree of one and a degree of two. So let's see, let's look at our table for horizontal Aston totes and see what we know about our degree. So we have a polynomial divided by a polynomial, Um, top his degree and bottom has degree end. So once again, we're just looking at our leading terms or leading coefficients. So our top is one. So we have m equals one and and equals two. So the degree of the numerator is one, and the degree of the denominator is too. So to match it up with this so m is less than and we have this situation, which means that our horizontal ascent tote has to be zero so we can produce just go where it's from. Their y equals zero is our only horizontal as him too.

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