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Use the zeros, vertical and horizontal asymptotes along with the sign of the function to sketch its graph.$$f(x)=\frac{x+1}{4 x^{2}-9}$$

Algebra

Chapter 1

Functions and their Applications

Section 7

More on Functions

Functions

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 the zeros, vertical an…

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Use a graphing utility to …

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Find the horizontal and ve…

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Make a hand-drawn graph. B…

02:29

Sketch a graph of each rat…

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Graph the rational functio…

to find the zeros of this functioning we needed at the numerator agricultural zero. But now the denominator since if the denominator we go to zero, this expression is manliness and we can see that X equals minus one. Satisfy this condition and hands f minus y equals to zero. To find the vertical ethnic jokes we need the denominator recalls shows Europe and another numerator and we can sector the denominator into two parts and then easy for us to say that when x echoes miners three, half of x equals 23 half satisfies this condition, enhance its function has two vertical s models which X equals two minus three halfs and X equals 23 halfs. To find the horizontal as mortals, we need to find the limit of this function that X goes to infinity. And since the numerator is upon a nominal outer one and the denominator is a phenomenon of the other two, so the denominator increases much more faster than numerator enhance. The new meter goes to zero. And here is a graph of this function. You can say that X equals two minus three halves and X equals 23 halfs at two vertical as models and why a cultural zero is horizontal as models and the only zeros are at X equals minus one.

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