Video: Finding the Equation of a Curve From a Sketch

Video Transcript

What is the function graphed in the given figure?

Looking at the direction of the arrows, this must be an odd function. And it’s decreasing left to right, so it must be negative.

Now we also know where it crosses the 𝑥-axis: negative three, negative one, and three. Those are the factors. So if we take these and set them equal to zero, those will be our factors. So if we would add over the negative three, we would have 𝑥 plus three equals zero, 𝑥 plus one equals zero, and 𝑥 minus three equals zero.

Therefore, the function that is being graphed is 𝑦 equals negative 𝑥 plus one 𝑥 plus three 𝑥 minus three.