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**Unformatted text preview: **f (x) = 2
x +1
to be a constant function since its domain is all real numbers (why?) and
2$$+ $
x2 $ 1
2x2 + 2
f (x) = 2
=
$ =2
x +1
x2 $$
$$+ 1
The following example uses linear functions to model some basic economic relationships.
$ 118 Linear and Quadratic Functions Example 2.1.5. The cost, C , in dollars, to produce x PortaBoy4 game systems for a local retailer
is given by C (x) = 80x + 150 for x ≥ 0.
1. Find and interpret C (10).
2. How many PortaBoys can be produced for $15,000?
3. Explain the signiﬁcance of the restriction on the domain, x ≥ 0.
4. Find and interpret C (0).
5. Find and interpret the slope of the graph of y = C (x).
Solution.
1. To ﬁnd C (10), we replace every occurrence of x with 10 in the formula for C (x) to get
C (10) = 80(10) + 150 = 950. Since x represents the number of PortaBoys produced, and
C (x) represents the cost, in dollars, C (10) = 950 means it costs $950 to produce 10 PortaBoys
for the local retailer.
2. To ﬁnd how many PortaBoys can be produced for $15,000, we set the cost, C (x), equal to
15000, and solve fo...

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