8.3 SAT Math - Graphing Functions

As we discussed under SAT Math Functions, the simplest way they will be tested in graphing is by the Vertical Line Test.  You should only hit one point if you draw a vertical line anywhere on the graph of a function; otherwise, you do not have a function.

Functions get a little more complicated than that as well.  Do remember that f(x) simply means y, so when graphing, that f(x) value is the same as your y value.  The trickiest way this is tested is by simply giving you the information f(2) = -1 or something similar.  Keep in mind that whatever is in the parentheses is your x value, and whatever f(x) equals is your y value – which means what you were given above is secretly the ordered pair (2, -1). 

Domain and range will obviously come up in graphing as well.  To find your domain on a graph, simply find the highest x value and the lowest x value.  The domain is everything in between and including those values.  To find your range, do the same with the shown y values.

Most of the math functions you'll be dealing with here are linear functions, which means they are the graph of a line.  Sometimes, you'll see other kinds of functions, like quadratic or absolute value.  It's good to recognize the graphs of more complicated functions right away so that you can eliminate answer choices.

Quadratic equations form parabolas in their graphs, which basically look like a big U.  They can be wide or narrow, right side up or upside down:

Graphs of Square Roots form half a parabola, since square roots are always positive.  They look like an arc:

Graphs of Absolute Value form a point: