Video Transcript
The function 𝑦 equals 𝑓 of 𝑥 is graphed on the 𝑥𝑦-plane shown. On the interval for how many distinct values of 𝑥 does 𝑓 of 𝑥 equal negative three-halves?
We’re looking for the places where 𝑓 of 𝑥 equals negative three-halves. On this 𝑥𝑦-plane, that’s the place where 𝑦 equals negative three halves because we know that 𝑦 equals 𝑓 of 𝑥. We could rewrite negative three-halves as negative one and a half and that it’s halfway between zero and negative three. We can mark negative three-halves along the 𝑦-axis.
We’ll draw the line 𝑦 equals negative three-halves. And then, we see that our function crosses this line in two places. And while we don’t know the exact values for 𝑥 when this function crosses negative three-halves, we do see two distinct points. And so, we can say, based on the given image, that there are two distinct values of 𝑥 when 𝑓 of 𝑥 equals negative three-halves.
