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Exercises Functions

Example 9 from Algebra and Trigonometry, 3.1 Functions and Function Notation

Finding an Equation of a Function

Express the relationship $2 n + 6 p = 12$ as a function $p = f (n),$ if possible.

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 express the relationship in this form, we need to be able to write the relationship where $p$ is a function of $n,$ which means writing it as $p = [expression involving n] .$

$\begin{array}{l} 2 n + 6 p = 12 \\ 6 p = 12 - 2 n & \begin{matrix} \end{matrix} Subtract 2 n from both sides . \\ p = \frac{12 - 2 n}{6} & \begin{matrix} \end{matrix} Divide both sides by 6 and simplify . \\ p = \frac{12}{6} - \frac{2 n}{6} \\ p = 2 - \frac{1}{3} n \end{array}$
Therefore, $p$ as a function of $n$ is written as

$p = f (n) = 2 - \frac{1}{3} n$

How did it go?

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From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 3.1, 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.