Alyssa R.
asked • 06/25/19Rational Functions
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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1 Expert Answer
I think Kevin's comment above is very good.
I would add the following.
Linear, quadratic...and in fact, polynomial functions of all degrees are continuous and differentiable on the the whole real line. So is the exponential function (which is in some ways not surprising considering the ability to express the exponential function as an infinite series). Also on any closed interval these functions are bounded.
The rational functions, however, are NOT continuous and NOT bounded. Rational functions are discontinuous and unbounded at zeros of the denominator.
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Kevin E.
The key to answering this exercises to examine the graphs of each type of function. Things to consider when discussing the similarities are: continuity of the graphs, the one to one nature of a function, etc. When discussing the differences, one can look at the equations in addition to the graphs. These equations describe what happens to each type of function over a specific range of x. For example, a line has a constant rate of change, but does a quadratic? Ask these questions of yourself as you approach the exercise.06/26/19