Example 3: Finding Values of Terms by Substitution

Let h be the function given by the rule

h(t) = t³ + 1.

t is a variable, h is a function, and h(t) is a term. The following expressions are also terms: h(½), h(x), h(t³), h(t³) + 1, h(t³ + 1), h(x) - h(t), h(t + Δt), h(t + Δt) - h(t). Find the values of each of these terms.

The values are computed by careful substitution.

The graph of h is given by the equation x = t³ + 1. In this equation, t is the independent variable and x is the dependent variable. In Figure 1.2.5, the five points

h(-1) = 0, h(-½) = ⅞, h(0) = 1, h(½) = 1⅛, h(1) = 2 are plotted and the graph is drawn.