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Stitz-Zeager_College_Algebra_e-book

we close this section with a new look at dierence

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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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