### Video Transcript

Determine ๐ evaluated at negative two.

In this question, weโre given the graph of a piecewise-defined function. And we need to use this graph to determine the value of ๐ evaluated at negative two. And to do this, we recall the ๐ฅ-coordinate of any point on our graph will be the input value of ๐ฅ and the corresponding ๐ฆ-coordinate will be the output of our function. For example, because our graph goes through the point with coordinates two, four, we can conclude that ๐ evaluated at two is equal to four. We want to evaluate ๐ at negative two. So our input value of ๐ฅ is negative two.

One way of doing this is to sketch a vertical line ๐ฅ is equal to negative two and determine the point of intersection with our graph. And we can see there are two possible points of intersection between the vertical line and the graph of our piecewise function. Thereโs the solid dot at the point negative two, zero, and thereโs the hollow dot at the point negative two, two. However, we can recall when thereโs a hollow dot on our graph, that means our function is not defined at this point and when thereโs a solid dot, our function does pass through this point. So, the graph of our function passes through the point negative two, zero. And therefore, ๐ evaluated at negative two is equal to zero.

Therefore, by considering the points of intersection between the given graph and the vertical line ๐ฅ is equal to negative two, we were able to show that ๐ evaluated at negative two is equal to zero.