c. Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.

Students should also be able to compose a function f(x) when the input x is also a function x(t), which simplifies to f(t) = f(x(t)). This just means substituting the entire function x(t) anytime the variable x appears in f(x). So if f(x) = x² and x(t) = t + 1, then f(t) = (t + 1)².

Students should also know that unlike their celebrity crushes, these functions have real-life applications. For instance, if T(y) is the atmospheric temperature as a function of height y and h(t) is the height of a weather balloon at time t, we can say T(h(t)) is the temperature of the location of the balloon at time t.