Homework Statement
So my book has a bunch of examples of graphs similar to sine or cosine graphs, where the maximums and minimums are the same (for example, the maximums might be 1, and the minimums will be -1). If I only have a graph to work with, I will just look at the waves and determine...
Thanks a lot for this post. I finally got it to work. I ended up using -1 though after ehild raised it as a possibility. I see that it would have worked with 0.5 too though.
I also corrected the mistake I made in my original work.
Thanks a lot guys!
The first one is 3x^2 - 1, and the second is 5x^2 - 1.
I just did the long division again, and this time I got a remainder of -1 + 2x. I don't understand what I'm doing wrong. I've successfully done long division of polynomials before this. I also read all the posts in this topic...
I put 0.5 in the original trinomial, and it equalled 0. But the question wants me to completely factor it. Doesn't that mean I need to use another tool to get the 2nd factor?
I tried doing the find a value of x that makes the polynomial equal 0, and I got 0.5 by trial and error, but when I then went to divide the trinomial in the original post by x - 0.5, I got a remainder. Doesn't that mean that x - 0.5 isn't a factor of the trinomial?
But how is that possible...
So I can't find an example in my book that shows how to factor a trinomial like this one:
2(x)^3 + 3(x)^2 - 1
I tried finding a number that multiplied to -2 and added to 3, but that didn't work. I then tried just factoring x out of the equation, but I didn't know what to do with the -1...
Maybe I don't understand what the symbols mean.
I understand "As x → -∞, f(x) → ?" to mean that as the values of x get larger negative (to the left), then the y value of the graph becomes what? Is that your question?
In my graph though, the y value, by that I mean f(x) goes down from y = 0...
So 1/f(x) is just a representation, or what they call a reciprocal function?
It's not as if all reciprocal functions are actually 1 / f(x)? It can be 2 / f(x) like in your bottom graph?I'm still confused about the "But that's only because as x gets very large positvely or negatively (x→±∞)...
Okay, now I'm confused about something else.
You said,
I don't understand how then in my graph of 1/f(x) on that curve part of the graph that points toward the top, and is positioned to the left of the y axis, right below the x axis, as x goes towards 0, y goes away from 0, but as x goes...
I just noticed something. Those three dots are at y = 0, because y is undefined for 1/0. Does that mean that it's just one horizontal asymptote at y = 0? Not three vertical asymptotes?
The reciprocal of a very small positive number is a larger positive number.
The reciprocal of a...
Homework Statement
The y = f(x) is the original graph. The question asks me to draw the y = 1/f(x) of that graph. What I did was just use the same x coordinates and then take the y coordinates and just do 1/y coordinate for each y coordinate. Is this the correct way to do it?
Also, the red...