In Exercises 57–80, follow the seven steps to graph each rational...

Question

In Exercises 57–80, follow the seven steps to graph each rational function. f(x)=4x/(x−2)

Accepted Answer

Draft a given rational function following the seven steps. Our function is F of X as equals to three X divided by X minus eight. So we'll check out the graphs in a little bit. But first, let's go to our seven steps. F M X equals to 3 x divided by X -8. Step one will be to determine symmetry. To determine symmetry. We will replace our X with negative X can see what we get as a result. If FX F negative X is equals to FX, we have X as symmetry, F F as negative of X is equals to negative F of X. We have origin symmetry. So we will check our symmetry by putting in negative X for X of native X. It's equals to three times negative X divided by negative X minus eight which gives us negative three X divided by negative X minus eight. This is not the same as our original. So we don't have Y axis symmetry and this is not the negative of our original. So we don't have origin symmetry either. This means we have no symmetry. Now you can check step two step two will be finding our Y intercept, we find the Y intercept by setting X equals to zero 0, 3, multiplied by zero, divided by 0 -8. That gives us 0 over -8, which simplifies the zero. Then we can check our X intercept. Check our X intercept. We set Y is equal to zero. We will say zero is equals to three X divided by X minus eight. Multiply both sides by X - to get rid of the denominator. This gives us zero. This equals to three X dividing both sides by three, gives us X equals to zero. So X intercept is also at zero. Now we find our vertical Asymptote to find this, we will set our denominator equal to zero and solve for X X -8 is equals to zero. This gives us X equals to eight. Cervical acid cell will happen at the line X equals to eight. Now, we need to find the horizontal asci code, find the horizontal Asymptote if you want to look at the degrees of our um our variables notice here we have X on top for a fraction and X on bottom. So both degrees are equal to what? Because both degrees are the same, we will divide the coefficients three divided by one gives us three. Pushing a horizontal ascent tode happens at Y as equals the three. Finally, number six, we will test out some values and plot them on our graph. So I make a table X F M X choose a few sample values negative 2 -1 one two, 16, 28. Plugging them into our equation, we all get out $3 by five, one third, negative three sevens N one 6 and 21/ step seven is finally graphing our function. We get a function that has no symmetry X intercept is zero, Y intercept is zero vertical Asymptote, X equals eight horizontal Asymptote Y equals three. And as our six points we created, if we were to look at our possible graphs, we can determine the answer to our problem is graph D, graph D has everything that we found, including our asymptotes and our points in no symmetry. OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 57–80, follow the seven steps to graph each rational function. f(x)=4x/(x−2)

Key Concepts

Rational Functions

Asymptotes

Graphing Steps

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