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

MA19.PRE.24

Compare and contrast families of functions and their representations algebraically, graphically, numerically, and verbally in terms of their key features. 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; asymptotes; and periodicity. Families of functions include but are not limited to linear, quadratic, polynomial, exponential, logarithmic, absolute value, radical, rational, piecewise, trigonometric, and their inverses.

Unpacked Content

Knowledge

Students know:
  • Properties of functions and make connections between different representations of the same function

Skills

Students are able to:
  • Compare properties of functions when represented in different ways (algebraically, graphically, numerically in tables or by verbal descriptions).

Understanding

Students understand that:
  • Each representation provides a unique perspective of the function.
  • Different representations are most appropriate for revealing certain key features of the function

Vocabulary

  • Function
  • Relative Maximum
  • Relative Minimum
  • Symmetry (Even/Odd)
  • End Behavior
  • Asymptotes
  • Intercepts
  • Increasing/Decreasing Intervals
  • Periodicity
  • Absolute Maximum
  • Absolute Minimum
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