Determining bounds of a function

[ptolema]

Homework Statement

decide if f is bounded above or below, and if f takes on maximum or minimum value
f(x)= x^2 for x< or =a, a+2 for x>a
on (-a-1, a+1), assuming a>-1

Homework Equations

x^2 is continuous on R

The Attempt at a Solution

I have no idea where to start with this. I can constrain a+2 to (-1, a+1), but I don't know how that applies to the bounds of the entire function.

 

[Mark44]

Homework Statement

decide if f is bounded above or below, and if f takes on maximum or minimum value
f(x)= x^2 for x< or =a, a+2 for x>a
on (-a-1, a+1), assuming a>-1

Homework Equations

x^2 is continuous on R

The Attempt at a Solution

I have no idea where to start with this. I can constrain a+2 to (-1, a+1), but I don't know how that applies to the bounds of the entire function.

Start by sketching a graph of this function. a is not given, so just pick some point on the positive x-axis and label it a. You might need to do this for several values of a, including at least one negative value.

Alternatively, you could choose a few specific values of a and graph this function for each of them, and see how the graphs are similar.

That's how I would start.