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 + 2

Accepted Answer

Hello everybody. Everything right today, today 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 function is G of X is equal to open parentheses, one divided by X closed parentheses, separate from the fraction plus eight. Now, the extras provided are all sets of different graphs showing a graph of F of X and a graph of GEO X. The X choice A has F of X with a point at one comma one and G of X with a point at one comma nine. A choice B has F of X with a point at one comma one and G of X with a point at one comma negative seven answer choice C has X with a point at one comma one and G of X with a point at nine comma one and answer choice D has F of X with a point at one comma one and G of X with a point at negative seven comma one. Now, since they specifically asked to use the transformation of the F of X function we should recall some rules that we have for transformation of functions and their graphs. So will recall that the graph oh Y equals F of open parentheses, X close parentheses plus C is the graph of Y equals F of X shifted C units up. So C in this case, is a constant or a number. And that's what the transformation for the F of X graph would be. That's how it's going to affect. In this scenario. I specifically chose this rule because in our scenario will say that if, if F of X, this is our scenario, if F of X is equal to one divided by X and GEO is equal to open parentheses, one divided by X closed parentheses plus eight, then G of X is equal to F of open parentheses, X closed parentheses plus eight. And therefore the F of X graph shifts. And now we just have to look at our rule. The C in this case will be the eight. So we will shift eight units up. So now we know that the Y value between the alpha X function and its graph will change eight units upwards for the G of X function and graph. So the point given every answer choice, the F of X function has a point out one comma one. Now, after undergoing the transformation, we know that we're shifting the graph eight units up. So the X value won't be affected. So we'll still have one comma something. Now, if we're moving eight units upwards, the Y component of our graph would change it with eight units as well. It'll be a plus eight since we're moving up. So we'll have one plus eight. So we'll have one comma one plus eight, which will turn into the point one comma nine. So if we start at an E X point of one comma one, and we shift that graph eight units upwards, we'll have a point at the G of X graph at one comma nine. So now we just have to look at our answer choices and see which one has that. And once we do that, we'll notice that answer choice. A has all of those quantities. They show us the F of X graph and the G of X graph where their F of X graph has a point at one comma one and their G of X graph has a point at one comma nine, meaning that they shifted the F of X graph upwards by eight units, which is exactly what we did. 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/x + 2

Key Concepts

Rational Functions

Transformations of Functions

Asymptotes

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