In Exercises 45–56, use transformations of f(x)=1/x or f(x)=1/x^2...

Question

In Exercises 45–56, use transformations of f(x)=1/x or f(x)=1/x^2 to graph each rational function. g(x)=1/(x−1)

Accepted Answer

Hello everybody. I have everything right today. And we're going to be looking at this question that states graph the given rational function using the transformation of F of X is equal to one divided by X where the given rational function is G of X is equal to one divided by open parentheses, X minus five, closed parentheses. Now the s provided all show different graphs showing F of X and G of X with each one having a point on that graph. So answer choice A has F of X with a point at one comma one and G of X with a point at negative four comma one A B has Avax with a point at one comma one and G of X with a point at six comma one. Answer choice C has F of with a point at one comma one and GEO X with a point at one comma negative four. And answer choice D has Frax with a points at one comma one and GEO ax with a point at one comma six. So since they specifically asked me to use the transformation of the F of X function, I should recall different rules that we have when it comes to transformations of functions and their graphs. So let's do exactly that. We can recall that the graph of Y equals F of open parentheses, X minus C closed parentheses is the graph oh Y equals F of open parentheses. X close parentheses, shifting, see units, right. So in this case, the C could be a constant or any number and it'll affect how we transform our function. Now, I write this specific rule because this is the rule that we will apply to our F of X and G of X functions. Because if a of is equal to one divided by X and GEO, X is equal to F of open parentheses, or do you have access equal to first, it's equal to one divided by open parentheses, X minus five, close parentheses, then this means that GEO is equal to F of open parentheses, X minus five closed parentheses. And therefore this will shift the aro vax graph five units, right? Because in this case, our, the number five is acting as the sea in our recall function. So since we're moving five units to the right, we know we're dealing with a change in the X value. And we noted that every graph of the F FX function has a point at one comma one in our answer choices. So if we shift that 65 units to the right, the X value will shift one plus five comma one because the Y value won't change since we're only moving horizontally. And this means that we'll have a point after we shift at six comma one. So six comma one will be our new point, our G of X point after we shift the graph of F of X five units to the right. So now that we have all this information, all we have to do is look at our answer choices and see which one has points that match this. And once we do that, we'll see that answer choice B shows exactly that they give us the graph of F of X, the graph of G of X and shows us that F of X has a point at one comma one N G of X has a point at six comma one which means F of X was shifted to the right by five units. So I hope that was helpful. And until next time.

In Exercises 45–56, use transformations of f(x)=1/x or f(x)=1/x^2 to graph each rational function. g(x)=1/(x−1)

Key Concepts

Rational Functions

Transformations of Functions

Asymptotes

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