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# Rational functions

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Rational functions for Pre-cal

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### Rational functions

1. 1. Rational Functions<br />By: Katie Thayer<br />
2. 2. A rational function is any function which can be written as the ratio of two polynomial functions.<br />What is a Rational Function?<br />
3. 3. Asymptotes<br />Asymptote - a straight line that is the limiting value of a curve<br />The red line on the graph indicates that y=x is the asymptote. <br />
4. 4. 2 types<br />There are two types of asymptotes. <br />Vertical Asymptote- x=___, ** CAN’T BE CROSSED**. Can be found be the zeros, or x- intercepts, which are in the denominator.<br />Horizontal Asymptote- y=___, ** Can be crossed*. But there are three different ways you can find a horizontal asymptote.<br />
5. 5. VA and HA<br />The Vertical Asymptote of out function would be, x=-3 and x=1<br />The Horizontal Asymptote is y=0.<br />
6. 6. Three types of Horizontal asymptote.<br />Type 1: when the degree of the denominator- degree being the exponential value of x- is larger than the degree of the numerator, then the HA is y=0.<br />Type 2: When the numerator degree and the denominator degree are the same , y=<br />The HA= y= <br />* When the power of the numerator is bigger than the denominator, the asymptote with be a slant, or oblique. To find the horizontal asymptote of these equations you have to use long division. <br />
7. 7. X-intercepts. <br />To find the x- intercepts you have to take the numerator and set it equal to zero. Going back to the first equation this is what find the x-ints, would look like. The you solve for x by dividing both sides by -5 . So you would get, and since zero can’t be divided , There are no x- intercepts.<br />
8. 8. Y- intercepts. <br />To find the y- intercepts you set x = to zero. And it equals 0, so the y- intercept would be at the origin, (0,0).<br />
9. 9. tables<br />To find possible points of where the line would cross on a graph, you make an x-y tables, of x’s to the left and right of each asymptote.<br />
10. 10. Domain and Range<br />The domain of a function is the set of all possible x values which will make the function "work" and will output real y-values<br />The range of a function is the possible y values of a function that result when we substitute all the possible x-values into the function.<br />
11. 11. The domain in the graph is (-∞,o)U (0,∞)The range would be the same.<br />
12. 12. Domain and Range cont.<br />The Domain of this function would be<br />D: (-∞,-3] U [-3,1] U [1,∞)<br />The Range would be (-∞,∞)<br />