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. h(x)=1/x2 − 4

Accepted Answer

Hello everybody. I have read everything right today that are 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 squared where our given function is G of X is equal to one divided by X squared as a fraction and outside of that fraction minus 11. Now the extras provided all give us different versions of the graph of alpha back. And geo answer choice A provides us a, the graph of F of X with a point at one comma one and the graph of G of X with a points at one comma negative as a choice B provides us the graph of FX with a point at one comma one and the graph of G of X with a point at one comma answer. Choice C provides us the graph of A of X with a point at one comma one and the graph of G of X with a point at negative 10 comma one. And as the choice D gives us the graph of Avax with a point at one comma one and the graph of GEO X with a point at 12 comma one. So we see that every answer to has the graph of F of X with common and pointing at one comma one. So that's an information that we will use later on in this question. So they gave us two different function F vax and GEO. In this case, A is our parent function because we're using that function to see how the transformation affects that graph. So we have that F of X is equal to one divided by X squared. That is our parent function. And our final function is GEO is equal to one divided by X squared and outside of the fraction minus 11. So that minus 11 functions as the transformation for a parent function. So we will therefore have that G of X. It's the same as saying GEO, X is equal to Apha vax minus because apple is one divided by X squared. So we can just replace that with apple back and we have minus 11 as transformation. And we know with rules of transformations that the graph of Y equals F of X minus C where C could be a constant or any number is the graph of F of X shifted C units down. So all that minus 11 does in our G of X function is move the graph of F of X 11 units downwards. So now it's when that common point comes into play. So we noted that every answer choice has F of X with a point at one comma one. So that is our starting point here. And then we shift 11 units down because we're doing minus 11. So that means that our Y value will go down by 11 units. So if we have one comma one and we shift 11 units down. If we move vertically down, we're only affecting the Y value. So our X will remain the same. So we'll have one comma and then if we move 11 units down, we're subtracting 11. So we have one comma one minus 11. Therefore, our new points will be at one comma negative 10. So we can use that information and the rule of transformation to see that answer choice. A gives us the correct transformation. Afro X has a point at one comma one and GEO X has a point at one comma negative 10 with both graphs having the same general shape except that Geo X has just been shifted downwards by 11 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. h(x)=1/x2 − 4

Key Concepts

Rational Functions

Transformations of Functions

Asymptotes

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