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/(x−3)^2+1

Accepted Answer

Wrap. The given rational function using the transformation of F of X is equals to one divided by X squared G of X is equals to one divided by X minus seven squared plus five. To solve this problem. We want to find our transformations. Now to do this, we wanna see if we have a horizontal translation and a vertical translation, horizontal will be if we have the form F of X plus C which means our graph is shifted see units to the left. Additionally, FX M AC on the outside will give us a shift C units down. Original FX is equals to one divided by X squared G M X one divided by X -7 squared plus five. Now we notice here, X minus seven squared X minus seven will shift this to the left or the right. Now, we said X plus C, we shifted C units to the left but we have X minus C which means we will shift this to the right. We then have a horizontal shift to the right seven units. Similarly, we also have a vertical shift with our plus five, we had minus C. In our example. Now we have a plus C. That means we will vertically shift this up and this is up five units. So we need a graph that has shifted to the right by seven units and shifted up five units. If we look at our possible graphs, we can then notice graph B as our exact translation to the right seven and top five. OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

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/(x−3)^2+1

Key Concepts

Rational Functions

Transformations of Functions

Asymptotes

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