From a given context, ascertain an explicit calculation, a recurring process, or calculation steps. Develop a function by combining standard function types using arithmetic operations, such as modeling a cooling body's temperature by adding a constant function to a decaying exponential. If T(y) represents atmospheric temperature as a function of height, and h(t) shows the altitude of a weather balloon over time, then T(h(t)) represents the balloon's temperature over time.

Write both recursive and explicit formulas for arithmetic and geometric sequences, utilize them to model situations, and convert between the formats. Understand the impact on the graph of substituting f(x) with f(x) + k, k f(x), f(kx), and f(x + k) for specified values of k; determining k from the charts. Utilize technology to test cases and illustrate an explanation of the graph's effects. Recognize even and odd functions from their charts and algebraic definitions.

Solve f(x) = c for a basic function f with an inverse and express the inverse. Validate that a function is another's inverse through composition. Interpret the values of an inverse function from a chart or a table, assuming the function is reversible. Create a reversible function from an irreparable