If h(x) is equal to ((x^2)-4)/(x+2) when x is not -2, and h(x) is continuous for all real numbers, then what is the value of h(-2)?

Question

1. 0

2. -2

3. -4

4. 2

5. This is impossible. There is an infinite discontinuity at x=-2

Answer 1

Are you working on limits?

x^2 - 4

---------- can be factored into

x+2

(x-2)(x+2)

------------

x+2

It seems as if the (x+2) on top would cancel with the (x+2) on the bottom leaving just x - 2

If you were looking for the LIMIT as x--> -2 then the answer would be to plug -2 into x (of the remaining x - 2) and get -4.

If you are looking for the exact value of h(-2), it does not exist because there is a small hole there in the graph with no corresponding y-value.

You can see this on your calculator if you have a graphing calculator. Ask it to graph [ (x^2 - 4) / (x+2) ] and then zoom in on the coordinates (-2, -4) You should see a small "missing" part of the graph, we often call a hole or a removable discontinuity.