Unformatted text preview: and x = 0. It is clear
from the calculator that the graph of y = f (x) is above the graph of y = g (x) on −∞, − 1
as well as on (0, ∞). According to the calculator, our solution is then −∞, − 2 ∪ [0, ∞) 4.3 Rational Inequalities and Applications 269 which almost matches the answer we found analytically. We have to remember that f is
not deﬁned at x = 1, and, even though it isn’t shown on the calculator, there is a hole1 in
the graph of y = f (x) when x = 1 which is why x = 1 needs to be excluded from our ﬁnal
Our next example deals with the average cost function of PortaBoy Game systems from Example
2.1.5 in Section 2.1.
Example 4.3.2. Given a cost function C (x), which returns the total cost of producing x products,
the average cost function, AC (x) = C xx) , computes the cost per item. Recall that the cost C , in
dollars, to produce x PortaBoy game systems for a local retailer is C (x) = 80x + 150, x ≥ 0.
1. Find an expression for the average cost function AC (x). Determine an appropriate ap...
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