Mathematics III Building Functions

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Build a function that models a relationship between two quantities. [Include all types of functions studied.]
1. Write a function that describes a relationship between two quantities
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.
Build new functions from existing functions. [Include simple radical, rational, and exponential functions; emphasize common
effect of each transformation across function types.]
3. 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); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the
graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
4. Find inverse functions.
a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse.
For example, f(x) =2x3 or f(x) = (x + 1)/(x × 1) for x ≠ 1.