SOLUTION: I had to sketch the graph of {{{f(x)+x^2-x-2}}} and I've done that and I understand everything from domain, range, axis of symmetry, x and y intercepts, minimum/maximum values and

Algebra ->  Functions -> SOLUTION: I had to sketch the graph of {{{f(x)+x^2-x-2}}} and I've done that and I understand everything from domain, range, axis of symmetry, x and y intercepts, minimum/maximum values and       Log On


   

Question 147155: I had to sketch the graph of f%28x%29%2Bx%5E2-x-2 and I've done that and I understand everything from domain, range, axis of symmetry, x and y intercepts, minimum/maximum values and continuous. But I don't really get what the problem is asking for when it say increases and decreases. It is not clear to me. Please help.
Answer by nabla(475) About Me  (Show Source):
You can put this solution on YOUR website!
Increasing means the slope is positive. Decreasing means the slope is negative. You can identify this easily via the graph. To do it without a graph you really need calculus for full effect.
So, let's look at the graph of f(x)=x^2-x-2:
graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+x%5E2-x-2+%29
We can see right away that the function is decreasing until x=1/2 (which is the vertex). After x=1/2 the function is increasing.
In interval notation we will say: D: (-infinity,1/2) I: (1/2,infinity). Furthermore, we can accurately describe x=1/2 as the minimum of the function due to the behavior around x=1/2.