MA19.PRE.26

Mathematics (2019) Grade(s): 09-12 - Precalculus

Students know:

Students are able to:

Determine horizontal, vertical, and slant asymptotes of rational functions, and use these to sketch the graphs, identifydomains and ranges, and end behaviors.
Sketch the graphs, analyze, compare, and identify domains and ranges of the basic trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.
Find the amplitude and period of a trigonometric function and use these characteristics to sketch its graph.
Identify and sketch translations of trigonometric graphs (vertical shifts and phase shifts).
Evaluate, graph and identify the domains and ranges of inverse trigonometric functions.

Students understand that:

A rational function is the ratio of two polynomial functions.
Rational functions contain restrictions on their domains and/or ranges. Therefore, their graphs contain asymptotes, holes, and/or discontinuity.
The graphs of rational functions vary, yielding various patterns.
Using algebraic methods to manipulate and/or solve the equation of a rational function can help determine important properties such as its zeroes, intercepts, asymptotes, domain, range, types of discontinuity, and end behavior.
Key characteristics (rational and trigonometric) of functions can help you visualize the sketch of it's graph and can lead to more effective and efficient graphing methods.