What does it mean when a number is large and positive/negative?
I'm trying to do cubic graphs and the book mentions checking what happens to y for large positive and negative values of x. I'm not entirely sure what that means. Can someone help me out? What does it mean by large?
Original post by chuchubee
I'm trying to do cubic graphs and the book mentions checking what happens to y for large positive and negative values of x. I'm not entirely sure what that means. Can someone help me out? What does it mean by large?
This means informally that x is sufficiently large that you only need consider the term in x^3 when thinking about the qualitative behaviour of your cubic - or in other words, (and slightly circularly!) x is sufficiently large that the term in x^3 is much larger than the other terms in the cubic.
For example, if you consider f(x) = -x^3 + x^2 + x, then for very large positive or negative x, the qualitative behaviour of f(x) is the same as the qualitative behaviour of -x^3.
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