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Section 3.4 : The Definition of a Function

4. Determine if the given equation is a function.

\[y = 14 - \frac{1}{3}x\] Show Solution

To directly determine if an equation is a function can be quite difficult at times. What we need to do is show that for each \(x\) that we plug into the equation we can only get a single \(y\) out of the equation. For this case we can kind of talk our way through this.

Look at the equation and notice that if we were to plug any \(x\) into the equation all we would do is multiply the \(x\) by \( - \frac{1}{3}\) and then add 14. For each of these algebraic operations there is exactly one number that results and so \(y\) can only be a single value regardless of the \(x\) we plug in.

Therefore, this equation is a function.