Question Video: Finding the Set of Zeros of a Linear Function Mathematics

Video Transcript

Find the set of zeros of the function 𝑓 of 𝑥 equals one-third times 𝑥 minus four.

The zeros of the equation will be the place where 𝑓 of 𝑥 is equal to zero. We want to know what we need to put in for 𝑥 so that the output of this function is equal to zero. To solve for this, we’ll need to get 𝑥 by itself. We need to isolate our 𝑥 variable.

First, we need to get rid of this times one-third. We can do that by multiplying the right side of the equation by three over one. Three over one times one over three equals one. But if we multiply the right side of the equation by three over one, we have to multiply the left side of the equation by three over one. Three over one times zero equals zero.

Now on the right, we bring down our 𝑥 minus four. One times 𝑥 minus four equals 𝑥 minus four. Bring down the zero. Now we add four to the right side of the equation. If we add four to the right, we must add four to the left. 𝑥 minus four plus four equals 𝑥. Minus four plus four cancels out. Zero plus four equals four.

Now we have four equals 𝑥, or the more common way we write it, 𝑥 equals four. What this means is if we take the value four and plug it in for 𝑥, four minus four equals zero; one-third times zero equal zero. When 𝑥 equals four, 𝑓 of 𝑥 equals zero. And that’s the only place that would create a zero. The set of zeros for this function contains only one value: four.