Mathematics (2019) Grade(s): 09-12 - Algebra II with Statistics

MA19.A2.17

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Note: Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximums and minimums; symmetries (including even and odd); end behavior; and periodicity. Extend to polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions.

Unpacked Content

Knowledge

Students know:

  • Techniques for graphing.
  • Key features of graphs of functions.

Skills

Students are able to:

  • Identify the type of function from the symbolic representation.
  • Manipulate expressions to reveal important features for identification in the function.
  • Accurately graph any relationship.
  • Determine when a function is even or odd.

Understanding

Students understand that:

  • Key features are different depending on the function.
  • Identifying key features of functions aid in graphing and interpreting the function.
  • Even and odd functions may be identified from a graph or algebraic form of a function.

Vocabulary

  • Polynomial function
  • Piecewise function
  • Logarithmic function
  • Trigonometric (sine and cosine) function
  • Reciprocal function
  • Radical function
  • Period
  • Midline
  • Amplitude
  • End Behavior
  • Intervals
  • Maximum
  • Minimum
  • Symmetry
  • Even and Odd
  • Intercepts
  • Intervals
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