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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.