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Use the zeros, vertical and horizontal asymptotes along with the sign of the function to sketch its graph.$$f(x)=\frac{6 x^{2}-6 x-36}{x^{2}-16}$$

Algebra

Chapter 1

Functions and their Applications

Section 7

More on Functions

Functions

Oregon State University

McMaster University

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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01:45

Use the zeros, vertical an…

01:07

Find the horizontal and ve…

02:13

Determine the vertical asy…

01:36

find all vertical and hori…

01:05

Sketch a graph of the func…

01:14

Find the vertical and hori…

02:36

Find the vertical asymptot…

01:54

Determine the vertical and…

to find the zeros of this function. We need that the numerator recalls to the rope and now the denominator. We can factor the numerator into two parts, and then it's easier to say that X equals two minus two and X equals 23 satisfies this condition and hence it has two zeros at X equals two manners to and access to three. To find the vertical as moto we need the denominator equals to zero, but not the numerator. We can also factor the denominator into two parts and then see there to say that X equals two minus four and X equals to four. Satisfy this condition enhance It has two vertical s models which are X equal to minus four. Hand X equals to four to find the horizontal has moved. Told in to find a limit of this function when X goes to infinity since both the numerator and the denominator upon a nominal of order to this limits is just as the ratio of the coefficients of the heads of the orders which is six. So why are you close to stakes? Is horizontal instrumental of this function? Here is a graph of this function, and they can see that these two right dot in eyes as a vertical is monitored. And this Harizat it'll writer dot in eyes horizontal as models. This black dotted line is y equals to zero, and we can say that there are two zeros at X equals two minus two and X equals 23

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