Question

HELP! I'll give A MEDAL!
How to find the graph which represents the function f(x):

Answer 1

It would help to know what f(x) is.

Answer 2

9x^2 - 36
over
3x + 6

Answer 3

You're looking for the graph of (3x-6), because when you factor out the top, you get [(3x+6)(3x-6)/(3x+6)]. And that's just a line that crosses the x axis at 2.

Answer 4

would the point be at 12 then?

Answer 5

What point? You have two points at which you cross either the x or the y axis. Neither is 12.

Answer 6

I thought this because it was the only option I have which crosses at 2...?

Answer 7

Was there more to the question that isn't posted? You asked for a graph. I gave you x and y intercepts. That point you have selected is very random, considering you didn't have anything to suggest a 12...

Answer 8

OHHH. No, I see what you were trying to come up with.

No, I didn't mean find the y value at x=-2. I was just stating there is an x intercept at 2 and the y at -6.

Answer 9

Ok, so then the opened circle on a graph would be on -2?

Answer 10

When you talk about graphs, you have to define whether you're talking about a point in reference to the x or y axis. The point is at (-2, -12), where -2 is the x and -12 is the y.

To find a y intercept for a line, in case this wasn't clear now that I reread the question, you set x equal to 0 to find y. So y= (3x-6) when x=0, is written as y=3(0)-6, which is also y=-6. So your y intercept is -6.

The x intercept is found by finding x when y is zero. (3x-6)=0 is written as -3x=-6, solving for x, x=2. Thus your x intercept is 2.

With these, you know the line crosses the points (2,0) [x intercept, where you find x and y is zero] and (0, -6) [y intercept, where you find y and x is initialized to zero].

As for the slope, you know that the slope form of a line is y=mx+b, which you are lucky to have given to you. In this case, y=3x+(-6). So your slope is 3/1, or 3.

And from that, you draw a line.

Answer 11

I'm going to stress again that you need to clarify what plane you are talking about when you refer to graphs. When you say (-2), we don't know which one you're talking about. Is it -2 on the y plane? On the x plane? When you get into Calculus, you have a z plane as well and that makes for three possible -2 options. It is very, very important.

Answer 12

Not to mention, on a two dimensional plane, you can't sit on just one plane. You must sit on a location of both the x and y simultaneously. This is a graph, not a numberline.

Answer 13

Sorry, this is just confusing to me. I meant -2 on the x axis. And +6 on the y axis ?

Answer 14

No, look at your graph again and look at my paragraph 5 replies up. I stated how to find the x and y intercepts. I won't rewrite that explanation until you pinpoint something specific, because I think it's pretty laid out.

That being said, at no point is a point ever on both (-2, 6) at the same time because those are intercepts. Intercepts, by definition, are where either x or y equals zero, but never both at the same time. (0,0) is the origin. (xintercept, y intercept) doesn't exist.

To summarize everything:
Solve for x=0 at a y intercept and you'll get (0, somenumber).
Solve for y=0 at an x intercept and you'll get (somenumber, 0).

Solve for slope with the equation y=mx+b, where m is a variable. You are given your equation in this format, so you don't need to do anything but look for your slope which is equal to the number M.

Then you can graph it. You aren't finding 'points' by solving for x and y. You're solving for intercepts. Points are found by plugging in random numbers and seeing what the other variable equals. For example:

y=3x-6, a point would be if I picked the point....let's say 30 to be my x.

So, y=(3)(30)-6.
y=90-6.
y=84.

So the point I found would be at (30, 84). It's completely randomly chosen numbers. X and Y intercepts are found by nothing by the equation. Does that make sense?