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Exercises Functions

Example 12 from Algebra and Trigonometry, 3.2 Domain and Range

Working with a Piecewise Function

A cell phone company uses the function below to determine the cost, $C,$ in dollars for $g$ gigabytes of data transfer.

C (g) = {\begin{matrix} 25 & if & 0 < g < 2 \\ 25 + 10 (g - 2) & if & g \geq 2 \end{matrix}

Find the cost of using 1.5 gigabytes of data and the cost of using 4 gigabytes of data.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
To find the cost of using 1.5 gigabytes of data, $C (1.5),$ we first look to see which part of the domain our input falls in. Because 1.5 is less than 2, we use the first formula.

$C (1.5) = $ 25$

To find the cost of using 4 gigabytes of data, $C (4),$ we see that our input of 4 is greater than 2, so we use the second formula.

$C (4) = 25 + 10 (4 - 2) = $ 45$

How did it go?

PreviousWriting a Piecewise Function Next Graphing a Piecewise Function

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 3.2, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.