How are rational functions similar to linear, quadratic, or exponential functions? How are they different? When are these similarities or differences important when looking for intersections between rational functions and other types of functions?
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Answer:
Rational functions are similar to all those other functions because they can contain all those other functions. Rational numbers are numbers that can be written as fractions, so we usually talk about rational functions as functions that are fractions with functions in the denominator and often the numerator. Either part of a rational function could contain a quadratic, linear, or exponential function.
This is significant when looking for intersections because it tells us how many points of intersection there might be and where. Quadratic functions are parabolas, which often have two points of intersection. Linear functions, or straight lines, may cross multiple times through other functions but don't contain curves themselves. Exponential functions have asymptotes that are significant in looking for intersections.
All these behaviors affect the shape of the rational function that results from the combination of other functions.
Step-by-step explanation:
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