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Chapter 1: Problem 17

Determine whether the equation represents \(y\) as a function of \(x .\) $$y=|4-x|$$

Short Answer

Expert verified
Yes, the equation \(y = |4 - x|\) represents \(y\) as a function of \(x\).

Step by step solution

01

Understand the Absolute Value Function

First, understand that the absolute value function, defined as \(|a| = a\) for \(a \geq 0\) and \(|a| = -a\) for \(a < 0\), always returns a non-negative number. This means that \(|4 - x|\) can produce any positive number or zero, depending on the value of \(x\).
02

Identify if there's more than one y for any x

Check if there are any values of \(x\) which give more than one corresponding value of \(y\). This can be done by examining the graph or thinking mathematically about the function definition. The result of an absolute value function is always positive or zero, and for each input \(x\), there is only one output for \(y\).
03

Final Determination

Since there are no values of \(x\) that gives more than one value of \(y\), the function \(y = |4 - x|\) represents \(y\) as a function of \(x\). In other words, each value of \(x\) corresponds to only one value of \(y\).

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Most popular questions from this chapter

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