How do you solve a graphing problem on STEP?

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Well, as with all STEP questions, each problem is unique. But with graphing problems there are some nice things you can do to help break down the problem. Firstly, ALWAYS DIFFERENTIATE, i cannot stress this enough. If you know how your gradient is changing, this gives a lot about what a graph looks like. Secondly, look for roots to both you equation and its derivative. This is a BIG part of these questions and where the most marks will be awarded. Find where your graph hits the y and x axis, and find where the fixed points are. Finally, once you have all your fixed points, make sure to note if they are a maximum, minimum or a turning point.

Now, you should have a pretty good idea of how your graph looks, but there's still one more thing we can do. Find what your graph looks like as it tends to +/- infinity

For example as y = e^x - x^3 tends to infinity, e^x will increase much faster than x^3, so will look a lot like e^x for large x

But for large negative x, e^x is essentially 0, so the graph will look pretty much like x^3

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