Determine 𝑓 of zero.
So here we have the graph of a function, which we have to use to evaluate that function when 𝑥 is zero. So let’s have a look at the graph. When 𝑥 is zero, there are two things going on: one thing happening around minus one; another thing happening up here.
Let me first explain what’s happening near minus one on the 𝑦-axis. When 𝑥 is less than zero, you can just read off the value of the function from the line to the left. Simply when 𝑥 is greater than zero, you can just read off in a normal way from the graph for the line going up to the right. But where those two lines meet, we’ve got an unfilled circle — somehow hollow. And that tells us that that point marked there does not appear on either of those lines; it’s not included on those lines. And so 𝑓 of zero is not equal to minus one as you might think.
Okay, so that’s one of the things happening when 𝑥 is zero on the graph. What about the other thing — thing on the top, the green circle there which was previously circled? So this circle is filled, unlike the other one. And it is this circle which tells us what the value of the function for this exponent is. So it tells us that 𝑓 zero is equal to three.
So there you go. A hollow circle in a graph shows a gap in that graph. And it’s the filled circle, which shows the value of the function for this value of 𝑥. And in our case, the value of the function when 𝑥 is zero, which is 𝑓 of zero, was three.