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.
