How To Tell If It Is A Function
Functions trip up a lot of students at first. Once you know the two tricks below, you can check almost anything fast, whether it shows up as a graph or a table.
There are two ways to check this, and it depends on whether you're looking at a graph or a table. Let's walk through both.
If they give you a graph
Draw a vertical line straight through the graph. Then look at how many times that line touches the graph.
If the line touches the graph more than once, it is not a function.
If the line touches the graph one time, it is a function.
This is called the vertical line test, and it is the easiest way to check a graph. You can slide that imaginary line across the whole graph in your head, or just check it at a few spots if the graph is curvy.
If they give you a table
Tables work a little differently. For a table, you look at the x values instead of drawing anything.
If an x value repeats, it is not a function.
If every x value is different, it is a function.
x | y |
1 | 5 |
2 | 3 |
3 | 8 |
2 | 4 |
4 | 1 |
Look at this table. The x value 2 shows up twice, once with y equal to 3 and once with y equal to 4, and that single repeat is enough to rule it out, so this table is not a function. If every x value only showed up one time, it would be a function.
That is really all there is to it. Use the vertical line test for graphs, and check for repeating x values in tables. Once you get used to looking for these two things, you will start spotting functions fast, even on a timed test.
Still feels a little fuzzy?
That is pretty normal, especially the first time you see it. Most students need to work through a few more examples before it clicks, and that is exactly what one on one tutoring is for. We just go problem by problem until it makes sense.
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