Question Video: Evaluating a Function at a Point from Its Graph If Possible | Nagwa Question Video: Evaluating a Function at a Point from Its Graph If Possible | Nagwa

Question Video: Evaluating a Function at a Point from Its Graph If Possible Mathematics • Second Year of Secondary School

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Determine 𝑓(0) using the graph below.

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Video Transcript

Determine 𝑓(0) using the graph.

Let’s look at the graph of our function. It must be a piecewise function, and this is because it’s made up of pieces of graphs of various functions over various intervals on 𝑥. For instance, let’s take the first portion of graph here. This portion is defined by a specific function over the interval from negative 10 to eight. In fact, we could even define this as the left-closed, right-open interval. And that’s because the solid dot tells us that it’s defined at 𝑥 equals negative 10 but not defined by this part of the function at 𝑥 equals negative eight. Then, the second part of the function allows us to define 𝑓 of 𝑥 at 𝑥 equals negative eight with the solid dot here.

But when 𝑥 is equal to zero, we can’t use this part of the graph to determine 𝑓 of zero. The empty dot tells us it’s not defined by this part of our function. So, how are we going to determine 𝑓 of zero? Well, when 𝑥 is zero, we’re looking for a part of the function that lies on the 𝑦-axis. We’ve already seen this can’t be defined by this function here, but we do have a solid dot here. And so, the function is actually defined when 𝑥 is equal to zero. This point has coordinates zero, four. So we see that 𝑓 of zero must be equal to four.

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