Algebra Know-It-ALL

Part Three 537

Answer 28-9

We can tabulate and plot several points in both functions including the real solution, (−1,0).
Table 30-4 compares some values of x, some values of the first function, and some values of
the second function. Figure 30-10 shows the curves and the solution point. On the x axis,
each increment is 1/2 unit. On the y axis, each increment is 5 units.

x

y

Solution

Figure 30-9 Illustration for Answer 28-8. The first function

is graphed as a solid curve; the second function

is graphed as a dashed curve. The solution point

has moved. To find its coordinates, we must solve

the new system algebraically. On the x axis, each

increment is 1/2 unit. On the y axis, each increment

is 2 units.

Table 30-4. Selected values for graphing the functions

y = (x+ 1)^3 and y = x^3 + 2 x^2 +x.

The bold entry indicates the real solution.

x (x+ 1)^3 x^3 + 2 x^2 +x

− 3 − 8 − 12

− 2 − 1 − 2

−1 0 0

0 1 0

1 8 4

2 27 18