Next, we plot the solution(s)
By examining Table 28-3, we can see that the span of absolute values for the input is
from 0 to 5, while the absolute values of the functions go up to 38. This time, let’s make each
increment on the x axis represent 1 unit, and each increment on the y axis represent 5 units.
With six divisions going out from 0 to the left and six to the right, that gives us an absolute-
value span from 0 to 6 for x, and that’s enough. For y, we have six divisions going up and eight
going down, and that’s sufficient to include all the function values in Table 28-3. Now that
we’ve decided on the dimensions of the coordinate grid, we can plot the three solution points
as shown in Fig. 28-3.472 More Two-by-Two Graphs
Table 28-3. Selected values for graphing the functions
y=x^3 + 6 x^2 + 14 x+ 7 and y= 3 x+ 1.
Bold entries indicate real solutions.
x x^3 + 6 x^2 + 14 x+ 7 3 x+ 1
−5 −38 −14
−4 −17 −11
− 3 − 8 − 8
− 2 − 5 − 5
− 1 − 2 − 2
0 7 1
1 28 4xy(–3,–8)(–2,–5)(–1,–2)Figure 28-3 Graphs of y=x^3 + 6 x^2 + 14 x+ 7 and y= 3 x+ 1.
The first function is graphed as a solid curve; the
second function is graphed as a dashed line. Real-
number solutions appear as points where the curve
and the line intersect. On the x axis, each increment
is 1 unit. On they axis, each increment is 5 units.