Chapter 7 Rational Functions - College of the Redwoods

716 Chapter 7 Rational Functions
y
10
y = 0
(2, 0)
x
10
x = 0 x = 4
Figure 4. Placing the horizontal and
vertical asymptotes and the x-intercept
of the graph of the function f.
At this point, we already have our function f loaded in Y1, so we can press the
ZOOM button and select 6:ZStandard to produce the graph shown in Figure 5. As
expected, the graphing calculator does not do a very good job with the rational function
f, particularly near the discontinuities at the vertical asymptotes. However, there
is enough information in Figure 5, couple with our advanced work summarized in
Figure 4, to draw a very nice graph of the rational function on our graph paper,
as shown in Figure 6(a). Note: We haven’t labeled asymptotes with equations, nor
zeros with coordinates, in Figure 6(a), as we thought the picture might be a little
crowded. However, you should label each of these parts on your graph paper, as we
did in Figure 4.
Figure 5. The graph of f as drawn
on the calculator.
Let’s now address part (b) by adding the horizontal line y = 2 to the graph, as
shown in Figure 6(b). Note that the graph of y = 2 intersects the graph of the
rational function f at two points A and B. The x-values of points A and B are the
solutions to our equation f(x) = 2.
We can get a crude estimate of the x-coordinates of points A and B right off our
graph paper. The x-value of point A is approximately x ≈ 0.3, while the x-value of
point B appears to be approximately x ≈ 4.6.
Version: Fall 2007