LAC 28:CXLII.2915. Building Functions

A. Build a function that models a relationship between two quantities. 1. Write a linear, quadratic, or exponential function that describes a relationship between two quantities. a. Determine an explicit expression or steps for calculation from a context. b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. B. Build new functions from existing functions. 1. Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k,both positive and negative. Without technology, find the value of k given the graphs of linear and quadratic functions. With technology, experiment with cases and illustrate an explanation of the effects on the graph that include cases where f(x) is a linear, quadratic, piecewise linear, absolute value, or exponential function. 2. Find inverse functions. Solve an equation of the form f(x) = c for a simple function f that has an inverse. Write an expression for the inverse.