I am having trouble with function notation, I don't know how to do it well.

Question

So I know how to graph things, and I know how to solve equations. but my problem is that I can't get the equation from graphs and therefore cannot solve them.

https://streamable.com/sa7al

Answer 1

Hi, Christopher,

Yours is a common difficulty, but it can be overcome with some practice. Getting the equation from a graph, of course, depends upon the type of graph (linear or parabola), but let's begin with the questions you posted, which do NOT require that you derive the formula:

(2) This one is a piecewise function made up of several partial linear functions. You are asked to find f(3) and f(-2). Remember that functions typically begin with f(x)= (some formula in the variable x). Therefore, f(3) means basically, find the y coordinate where x=3 . Notice on the graph that the point (3,-3) is on the line. Therefore, f(3)=-3. Likewise, looking on the graph where x=-2, you can see that the coordinates are (-2,1), so f(-2) = 1.

(3) The second graph contains a parabola and a line, but the process is the same. For f(2), find the spot on the graph where x=2. Note that this is where the parabola stops and the line begins. The line has a darkened circle at that point, so use the point (2,1), so f(2)=1. For f(0), do the same. The point where x=0 seems to be at the vertex of the parabola, where y=1, so f(0)=1

Best wishes!

Answer 2

The examples that you linked ask only for the value of a function at one point.

The typical plot is on the "x-y plane", where x is the independent variable and y is the dependent variable. The corresponding notation is "y = f(x)", meaning that y is a function of x. In other words: if you know the value of x, you can find the value of y.

You can define a function with a graph, or with one or more equations. There might also be conditions applied: e.g. a function definition could be:

y = x, for x > 0

y = -x, for x < 0

Note in this example that y is not defined when x = 0

What I'm describing above are called "conventions"---these are not hard and fast rules, but simply ways of writing things that are internally consistent.