The simplest rational function that we know is f(x) = 1/x. Here is its graph.

Knowing the shape of this basic function, we can know graph more complex rational functions by using transformations of f(x) = 1/x. For example:

We are going to give you a trick that you might use when solving more complex functions, we are going to explain how to use it and we are going to give you some examples.

“YHTVX” That stands for: “whY His TV eXploded”.

**Y** y-intercepts; you set x equal to zero and solve for y.

**H** Horizontal Asymptotes

-If you have an x with a higher exponent in the denominator than the numerator, your HA is zero.

-If both x have the same exponent, you divide their coefficients and the result is your HA value.

-If the x exponent from the denominator is greater than the one in the numerator, you make a division, you ignore the reminder and you take the quotient as your “slant asymptote”.

**T** Touch or togetherness

-If you have an x with a higher degree than one, in the numerator, you are touching the HA at this point of x.

-If you have an x with a higher degree than one in the denominator, both curves of the equation will be together at this particular Vertical Asymptote.

**V **Vertical Asymptotes; set the denominator equal to zero and solve for x.

**X **X-intercepts; set the numerator equal to zero and solve for x.

EXAMPLES:

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