RatF - Rational Functions Module Overview
Rational Functions Module Overview
Introduction
You have been introduced to polynomial functions in previous lessons. They are used in many facets of life. More functions that now will be covered are rational and radical functions. Many people have an interest in pastimes such as diving, photography, racing, playing music, or just getting a tan. Other people are considering a career in medicine, machinery, farming, banking, or weather. Radicals involve roots of a number, and rational functions have expressions written as a fraction. Pressure in diving, exposures in photography, average speed in racing, frequency in music and the sun's radiation can all be expressed as a radical or rational function. The careers listed are a few examples of jobs that use radical or rational functions in various aspects. Rational functions will be explored here.
Essential Questions
- How are rational expressions multiplied and divided?
- How are rational expressions added and subtracted?
- How are complex fractions simplified?
- How are rational equations solved?
- Why are all solutions not necessarily the solution to an equation? How can you identify these extra solutions?
- How are rational functions graphed?
- In solving rational and radical equations, what are extraneous solutions?
- What are the key features of the graphs of rational functions?
Rational Functions Key Terms
Rational Expression - An expression that can be written as a fraction.
Excluded Values - Values that make the expression undefined (0 in the denominator).
Like Terms - Terms having the exact same variable(s) and exponent(s).
Extraneous Solutions - Solutions that make the expression undefined.
Intercepts - Points where a graph crosses an axis.
Domain - The values for the x-variable.
Range - The values for the y-variable.
Zeros - The roots of a function, also called solutions or x-intercepts.
Asymptotes - Vertical and horizontal lines where the function is undefined.
Extrema - Maximums and minimums of a graph.
End Behavior - The rise or fall of the ends of the graph.
Conjugate - The same binomial expression with the opposite sign.
Greatest Common Factor - Largest expression that will go into the terms evenly.
Lowest Common Denominator - Denominator that is the smallest multiple of all of the denominators.
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