SOLUTION: Find intervals on which the given function is increasing and the intervals on which it is decreasing. f(x) = x^2 +1 I've tried to solve this and I've looked for examples througho

Algebra ->  Functions -> SOLUTION: Find intervals on which the given function is increasing and the intervals on which it is decreasing. f(x) = x^2 +1 I've tried to solve this and I've looked for examples througho      Log On


   

Question 83400: Find intervals on which the given function is increasing and the intervals on which it is decreasing.
f(x) = x^2 +1
I've tried to solve this and I've looked for examples throughout my textbook. I just can't seem to understand how to do it.
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
The graph of y=x^2 is a parabola that opens upward. Therefore, y=x%5E2+%2B1 is that same parabola that opens upward, but it is moved UP one unit. It looks like this:
graph%28300%2C300%2C+-6%2C+6.5%2C+-4%2C8%2Cx%5E2%2B1%29+

A graph is increasing if when you move along the graph from LEFT to RIGHT, the y value becomes larger, and it is decreasing if when you move from LEFT to RIGHT the y value becomes smaller. From looking at the graph, notice that the graph is DECREASING on the left side of the graph, and INCREASING on the right side of the graph. Therefore, it is DECREASING from -infinity to x=0, and it is INCREASING from x=0 to infinity.

R^2 at SCC