In Example 8, change x² − 3x to x³ + 4x and then determine the statements that should be placed in the three boxes in Fig. 3.3.

Data from Example 8

The function f(x) = x² − 3x tells us to “square the input, multiply the input by 3, and subtract the second result from the first.” An analogy would be a computer that was programmed so that when an input number was entered, it would square the number, then multiply the number by 3, and finally subtract the second result from the first. The result would be the output. This is diagramed in Fig. 3.3.

The functions f(t) = t² − 3t and f(n) = n² − 3n are the same as the function f(x) = x² − 3x, because the operations performed on the independent variable are the same

Input Square X x f(x)=x-3x Multiply by 3 X Fig. 3.3 x, 3x Subtract 3x from x x-3x Output