## There are several questions in the math section that ask how to graph a certain function. For example this, this, and this. How do you answer these questions?

One approach is below:

#### Explanation:

I have an approach that I use when answering these questions that may be helpful to follow.

The first thing to know is that I tend to use a lot of graphs as I build up to the question posed. The engine powering Socratic doesn't (or hasn't in the past) liked having more than a couple of graphs being open while working on another, and so I'll build one and then save it by adding a letter into the graph. So for instance the command for the graph has "graph {...}" and so I'll add an "a" after "graph" to in effect save it. Right before I post the answer, I delete the extra letters and all the graphs come up.

The first thing I'll show is the base graph for a given function. Let's say we're looking to graph $y = - {x}^{2}$. I'll show the base graph:

graph{x^2}

And then I'll discuss how we're changing it (so for the example I'd talk about how the function is given a negative value and so the graph will look the same but be inverted downwards) - and then show the graph:

graph{-x^2}

Of course, the more complicated the function, the more graphs and explanations as to how the graph is changing and why (I'll have 4 or 5 graphs on a trig graph, for example).