How do you know if the graph starts from above or below?

Question

I can't seem to find a way to know if a graph starts from below or above. By that I mean what is pictured below (where the graph starts from the top left).

For example, in this graph below where the equation is as in the picture, I know that the x values are 0, 1 and 3 but I'd have thought that the graph would start from the bottom left quadrant due to the fact that the x is positive. Could someone please explain why in this case it starts from the top left and how to know for other similar cases.

Any help is appreciated, thank you.

If you are asking why $y>0$ when $x<0$, it is because $x^2>0, $x-1<0$, $x-3<0$ and "a negative times a negative is a positive." If this isn't what you're asking, please clarify the question. — saulspatz, Dec 14 '20 at 17:56
The notion of such a graph "starting" is non-sensical. You can plot it in any order, or piecemeal, if you like. — David G. Stork, Dec 14 '20 at 17:58
I simply came for some help. Please tell me how I should have phrased it. @DavidG.Stork — Gravity098, Dec 14 '20 at 18:08
@saulspatz Sorry for any confusion, the answer to what I meant is below. Thank you though! — Gravity098, Dec 14 '20 at 18:09
So, @Gravity098: given you accept the "answer" below, tell us all: Does your graph start "from above" or "from below"? — David G. Stork, Dec 14 '20 at 18:59

score 2 · Accepted Answer · answered Dec 14 '20 at 17:58

2

Let's get a few simple examples.

Mathematica graphics

Notice that odd powers have one behaviour at the ends and even powers have the opposite behaviour. This continues for higher powers.

You want to graph $$ x^2(x-(\text{don't care}))(x-(\text{don't care})) \\ = x^4 + (\text{don't care}) \text{.} $$ So we expect even power behaviour.

This is exactly what we do when the leading coefficient is positive. When it is negative, flip the graphs upside-down.

Mathematica graphics

answered Dec 14 '20 at 17:58

Eric Towers

67,037

Thank you very much! – Gravity098 Dec 14 '20 at 18:10
I don't see how @EricTower's "answer" addresses the stated question. So, Eric, does the given graph start "from above" or "from below"? Please refer to the red circle in the OP's problem statement. Thanks. – David G. Stork Dec 14 '20 at 18:41

How do you know if the graph starts from above or below?

1 Answers1