[F.LE.] Linear, Quadratic, and Exponential Models

Objectives

Construct and compare linear, quadratic, and exponential models and solve problems.

• • F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.

  • F.LE.1a Prove that linear functions grow by equal differences over equal intervals; and that exponential functions grow by equal factors over equal intervals.

    • F.LE.1b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

    • F.LE.1c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

• F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

  • F.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

Interpret expressions for functions in terms of the situation they model.

• F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context.

  • F.LE.6 Apply quadratic functions to physical problems, such as the motion of an object under the force of gravity. (California Only)