How do you read the graph of a function?

Question

I can interpret functions in the formula form but I simply can’t understand how it can become a graph. How would you transform one into the other?

In: 46

Answer 1

Imagine you have a function like f(x) = x^2.

You can think of the graph of the function as all the pairs of numbers: (x, f(x)). In the specific case of this function, that’s the pairs of numbers (x, x^2).

For example, (2, 4) and (3, 9), and (67.23, 4519.8729) are all points in the graph of the above function.

If you consider all pairs of numbers (x, f(x)), you get the graph of the function. Take a plane with an x-axis, and a y-axis, and plot the pairs of numbers: x on the x-axis, and f(x) on the y-axis.

Now obviously you can’t plot every pair of numbers since there are an infinite amount of them, but what you can do is take some of the integers values and plot them. In the case of (x, x^2), we have:

(-4, 16), (-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4), (3, 9), (4, 16) and so on.

Then draw a curve that goes between these points, and you have a visualisation of the graph of a function. The actual graph is all values (x, x^2), however.

In fact, the graph of a function is sufficient to describe the function completely!