 Functions are often presented in graphical form. The graph of y equals f of x is the graph whose points are xy, where y is equal to f of x. So, for example, we might sketch the graph of y equals f of x, where f of x has the following values. So, remember, the graph of y equals f of x consists of all points xy, where y equals f of x. And so, if we look at our table, we see that if x equals negative 2, f of negative 2 is equal to 3. So, negative 2, 3 is on the graph, so we can graph it. And remember, if it's not written down, it didn't happen. Always label your points and graphs. If x equals negative 1, f of negative 1 is negative 1, so negative 1, negative 1 is on the graph. If x equals 0, f of 0 is 2, so 0, 2 is on the graph. If x equals 1, f of 1 is 5, so 1, 5 is on the graph. If x equals 2, f of 2 is 4, so 2, 4 is on the graph. We could connect the dots, but we have no evidence that there are any other ordered pairs, x, y, where y equals f of x. And so, at this point, we only know that the graph consists of these five discrete points. And again, if it's not written down, it didn't happen, so we should label this as the graph of y equals f of x. An important thing to be able to do is to be able to read values off the graph. So, let's say we have the graph of y equals f of x. We want to find f of 3. So, it's important to remember, equals means replaceable. We want to find f of 3. Since this is a graph of y equals f of x, we can replace x with 3. And so, f of 3 is the y-coordinate of the point of the graph where x is equal to 3. So, we look on the graph and we see the graph passes through the point 3, 5. So, x equals 3, y equals 5, but equals means replaceable. y is equal to f of x, so f of x is equal to 5. But equals means replaceable. x is equal to 3, so we can replace x with 3 and get f of 3 equals 5. Another way we can use this as the following. The graph is shown. Let's solve f of x equals 0. So, we want to solve f of x equals 0. Equals means replaceable. y is equal to f of x, so that's y equals 0. And we see the graph passes through two points where y is equal to 0. The points negative 2, 0, and 3, 0. At negative 2, 0, x is negative 2, y is 0. So, y is equal to 0. Equals means replaceable. y is equal to f of x, so f of x equals 0. But equals means replaceable. x is equal to minus 2, so replacing x with minus 2, we get f of minus 2 equals 0. And so we can say that x equals negative 2 solves f of x equals 0. Or f of x equals 0 when x equals minus 2. But wait, there's more. That's second point 3, 0. At 3, 0, x is equal to 3. y is equal to 0. Equals means replaceable. So, y is equal to f of x, so we can replace y with f of x and get f of x equals 0. Equals means replaceable. x is equal to 3, so we can replace x with 3 and get f of 3 equals 0. And so we can say x equals 3 solves f of x equals 0, which gives us a second solution. Now, because the accuracy of reading numbers off a graph is limited, then we're often more interested in more general questions about the values of functions. So, for example, the graph of y equals f of x is shown. We might be interested in when f of x is greater than 0. And so we want f of x greater than 0, but equals means replaceable. y is equal to f of x, so I can replace f of x with y. And so we want to find where y is greater than 0. But a point has y greater than 0 when it is above the x-axis. And so all of these points will have y greater than 0. And we can describe this in interval notation. We see that for x in the interval 2 to 5, y is greater than 0, and so f of x is greater than 0.