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

MA19.PRE.25

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Extend from polynomial, exponential, logarithmic, and radical to rational and all trigonometric functions.

Unpacked Content

Knowledge

Students know:
  • Techniques for graphing.
  • Techniques for finding a rate of change over an interval on a table or graph.
  • Techniques for estimating a rate of change over an interval on a graph.

Skills

Students are able to:
  • Calculate average rate of change on a specified interval when given an equation or table ofa polynomial, exponential, logarithmic, and radical to rational and all trigonometric functions.
  • Interpret the average rate of change of a polynomial, exponential, logarithmic, and radical to rational and all trigonometric functions in the context of a problem when given symbolic representations, tables, graphs, or contextual situations.
  • Estimate the average rate of change for a specific interval of a polynomial, exponential, logarithmic, and radical to rational and all trigonometric functions functions when given agraph.

Understanding

Students understand that:
  • The rate of change is the ratio of the change between the dependent and independent variable.

Vocabulary

  • Average rate of change
  • Specified interval
  • Difference Quotient
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