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Example 3: Finding Values of Terms by Substitution
Let h be the function given by the rule h(t) = t^{3} + 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(t^{3}), h(t^{3}) + 1, h(t^{3 }+ 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 = t^{3} + 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. Figure 1.2.5


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