## Tutoring on Determining Key Components of Rational Functions

Learning Objectives:

#### Understand to Determine Rational Function Values.Understand to Determine Asymptotes and Graph Rational Function.

Math Tutoring on Determining Key Components of Rational Functions

A Rational Function is a function f can be described as a quotient of two polynomials f(x) = p(x) / q(x) , where  q( x )is not the zero polynomial, where the domain of the Rational Function would be all the values of x  that do not make q( x) or the denominator equal to zero.  If x = a is a vertical asymptote, as x approaches the value of a, f (x)or y approaches either positive infinity or negative infinity, meaning the graph will go up indefinitely or down indefinitely as it approaches a vertical asymptote. Now let us talk about horizontal asymptotes. Horizontal asymptotes are horizontal lines that the graph approaches as x approaches either positive infinity or negative infinity. So for horizontal asymptotes, we are going to see how the function behaves as x increases or decreases without bound. One way to help us determine the horizontal asymptote in math tutoring is to think as the numerators and denominators racing to infinity. If we could determine whether the numerator or denominator wins, which will help us determine the equation of the horizontal asymptote.

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Hook Questions:

1.    How do you graph a function?

2.    What is a rational function?

3.    How do you find the horizontal asymptote of a rational function?

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