Question

how do I give a formula for the extended function that is continuous at x=-2

Answer 1

What do you mean by extended function? Can you give the exact wording of the question?

Answer 2

Let f(x)=(x^2 + x - 2)/(x^2 +7x + 10)
Give a formula for the extended funciton that is continuous at x = -2

Answer 3

Ok, so they want you to "extend" the function by declaring that it's equal to something or other at -2, so that it becomes continuous. So first you need to find the limit of f(x) as x approaches -2. Do you know how to do that?

Answer 4

I've done it, but I'm not good at it. do I need a graph?

Answer 5

Sorry, lost internet for a second there. You don't need a graph, just divide out that rational function, and see what happens. You need to find a way of evaluating the function at x=-2, without actually evaluating it, since it's undefined there. That's really unclear, I know, but see what you come up with.

Answer 6

Ok, so would I do ((x - 1)(x + 2))/((x + 2)(x+5) and then plug -2 in for x?

Answer 7

Not quite - cancel out the x+2's first. That will allow you to evaulaute it.

Answer 8

Aren't they asking for a formula though? So should I just leave it as (x-1)/(x+5)?

Answer 9

No, what you want is to just hand them back the equation they give you, but add in one point: the point where x=-2, when the function isn't defined. There's a hole in the graph at that point, but the hole is at a certain y-value. So plugging in x=-2 now will let you find that y-value. Here's a picture of all that: