UP:MA19.PRE.26
Vocabulary
- Rational functions
- Horizontal asymptote
- Vertical asymptote
- Slant asymptote
- Amplitude
- Period
- Phase shift
- Domain
- Range
- Frequency
- Midline
Knowledge
Students know:
- Techniques for graphing,
- Key features of graphs of functions.
Skills
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.
Understanding
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.
