I can interpret functions in the formula form but I simply can’t understand how it can become a graph. How would you transform one into the other?
In: 46
Making a graph is really handy to “see the big picture” of a formula. The example we’ll use is y=x*2.
| If x is | Y would be |
|—|—|
| 0 | 0 |
| 1 | 2 |
| 1.5 | 3 |
| 2 | 4 |
| 3 | 6 |
A graph basically does the same thing as that table, but for more numbers. Start with a dot at “0 steps the the right” and “0 steps up” (0,0). Then the next dot goes at “1 step to the right, 2 steps up” (1,2). Then a dot at “1.5 (total) steps to the right, and 3 (total) steps up” (1.5,3). Another dot at (2,4) and a fifth dot at (3,6).
That’s how you plot just those exact answers, but what if we want more dots than that? Well, you can do the math for what y would be when x is 2.5, and 3.5, and 2.75, and 2.6373847… and if you did the math for every little infinite number, eventually all the dots would be touching and form a line. **The magic of graphs is that if you just make a few dots, you can usually eyeball drawing the line, without having to do infinite math.** If you plot just that table, you should notice that the dots are all in a line. And if you try to draw a nice straight line connecting all of those dots, you’ll find that if you do the math for x=2.5 (2.5,5), the dot ends up being on the line you drew!
Going from the graph to the function is trickier, it mostly breaks down to recognizing the overall shape of the graph, straight lines, vs lines with 1 curve vs lines with two curves, etc. And then using some exact numbers to work backwards.
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