Find inverse functions. Solve an equation of the form 𝑦 = 𝑓(𝑥) for a simple function f that has an inverse and write an expression for the inverse. Verify by composition that one function is the inverse of another. (Algebra II) Read values of an inverse function from a graph or a table, given that the function has an inverse. (Algebra II) Produce an invertible function from a non-invertible function by restricting the domain.
Identify the effect on the graph of replacing 𝑓(𝑥) by 𝑓(𝑥) + 𝑘,𝑘 𝑓(𝑥), 𝑓(𝑘𝑥), and 𝑓(𝑥 + 𝑘) for specific values of 𝑘 (𝑘, a constant both positive and negative); Find the value of 𝑘 given the graphs of the transformed functions. Experiment with multiple transformations and illustrate an explanation of the effects on the graph with or without technology.