Curriculum placement
Precalculus. This describes the skill, not a learner estimate.
Asymptotes, holes, and intercepts
Analyze holes asymptotes intercepts and domain of rational functions
Problem types
- Behavior on each side of a discontinuity
- Asymptotes, holes and intercepts of a rational function
Builds on
- Operations on rational expressions
- Domain and range
- Fundamental theorem of algebra · Useful idea
The number of zeros of the numerator and denominator gives the x-intercepts and vertical asymptotes of a rational function.
- Dividing polynomials · Earlier idea
Dividing the numerator by the denominator shows the long-run behavior of a rational function, such as a slant asymptote.
- Rational equations with one denominator · Useful idea
Solving a rational equation finds where the graph of a rational function takes a value.
Leads to
- Comparing functions given in different forms · See it applied
Features of a rational function are compared in its equation, table and graph.
Related skills
- Conic sections and their equations · Related idea
The function y = 1/x is a hyperbola with the axes as asymptotes, a conic section.
- End behavior of a polynomial · Related idea
A polynomial's degree and leading coefficient set its end behavior. A rational function compares the degrees and leading coefficients of its numerator and denominator to find its horizontal asymptote.
- Solving rational equations · Related idea
The inputs that make a denominator zero are the holes and vertical asymptotes of the graph. They are also the excluded values that must be checked when solving a rational equation.
- Piecewise and absolute-value functions · Related idea
A function may act differently on each side of a point, as a rational function approaches different values from the left and right.
- Composition of functions · Shared foundations
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