Attributes of Rational Functions

Attributes of Rational Functions

By Dee Pickle

What did you notice? Did you try plugging in the x-intercept values? What happens if you plug in x= -1? x = 0? Do you get zero in the numerator or the denominator?​

​So what conclusion can you come to about the zeros of the graph and the equation of the graph? What is the value of y when you have an x-intercept?

​It is easy to find a y-int with the graph in front of you, but what if it wasn't there? If you only have an equation and you are asked to find the y-int, what can you do? Can you plug in a certain value for x and solve for the y-int? If so, what value of x are you plugging in?

​Does this process for finding the y-int work for every function?

​Again, I encourage you to pay attention to the attributes in the graph. At what values are they happening? Are they x or y? What happens if you plug the values in? Do you create a value of 0? Is it in the numerator or denominator?

​Read the question below the graph. This equation is distinctly different than the others and there is a distinctly different attribute showing up in the graph because of it. What do you see?

​Switching to horizontal asymptotes changes what to pay attention to in the equation.

Instead of finding zeros, pay attention to the degree of the numerator and the denominator. ​

​What happens when the degree of the top is bigger than the bottom?

Smaller?

What if the degrees are the same? Compare the graphs with horizontal asymptotes to answer these questions.​

​Again, the answer you seek is found in comparing the degree of the numerator and denominator.

​Pay attention to the degree of the numerator and denominator again. Also, what is so different looking about this graph compared to the others?

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• TRUE

• FALSE

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Choose the answer(s) you believe to be correct.

• Holes happen because at that value of x, the function value becomes 0/0

• Holes do not happen

• Vertical Asymptotes happen when the numerator is 0