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Exercises Functions

Example 3 from Algebra and Trigonometry, 3.6 Absolute Value Functions

Finding the Zeros of an Absolute Value Function

For the function $f (x) = | 4 x + 1 | - 7,$ find the values of $x$ such that $f (x) = 0.$

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
$\begin{matrix} 0 & = & | 4 x + 1 | - 7 & Substitute 0 for f (x) . \\ 7 & = & | 4 x + 1 | & Isolate the absolute value on one side of the equation . \\ 7 & = & 4 x + 1 & or & −7 & = & 4 x + 1 & Break into two separate equations and solve . \\ 6 & = & 4 x & −8 & = & 4 x \\ x & = & \frac{6}{4} = 1.5 & x & = & \frac{- 8}{4} = - 2 \end{matrix}$

The function outputs 0 when $x = \frac{3}{2}$ or $x = - 2.$ See Figure 8.

Figure 8

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

For the function $f (x) = | 2 x - 1 | - 3,$ find the values of $x$ such that $f (x) = 0.$

How did it go?

PreviousWriting an Equation for an Absolute Value Function Given a Graph Next Identifying an Inverse Function for a Given Input-Output Pair

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 3.6, 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.