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Find all the asymptotes and plot the graph of the given function.$$g(x)=\frac{4 x^{3}-2 x^{2}+3 x-5}{x^{2}-9}$$

Vertical asymptote: $x=-3, 3$. Slant asymptote: $y=4x-2$

Algebra

Chapter 1

Functions and their Applications

Section 7

More on Functions

Functions

Missouri State University

Campbell 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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find all vertical and hori…

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Determine the vertical asy…

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Find the vertical asymptot…

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Find all asymptotes for th…

to find the vertical. As mom told of this function, we need the numerator to be 90 and the denominator to be zero. And hence we have two solutions which are X equals minus three and X equals three. Is that two vertical s more photos of this function. We'll assume the slant. Asthma told of the function is y equals a X plus B. And according to the instruction given by the book, Well, that l Because I man is cute. And this simple calculus, we can have this expression we need. L go through there. Oh, as X goes to infinity, since when l goes through their f x goes to kill X and this is the definition of asthma tote. So to guarantee that l goes to zero as X goes to infinity, we need the coefficient of the execute B zero and the coefficient of the X squared B zero as well. So we get two equations for these two conditions and solve these two equations gives us A equals four and B equals minus two. So the snap s Mementos of this equation is y equals four X minus two. This is a graph of the bowel function this right dotted nice as vertical as Mementos and the snack as move told

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