Summarize all pertinent information and sketch the graph of y = f(x):
f(x) = sqrt (25-x^2)

Question

anonymous · Answer

Anyone there?

anonymous · Answer

Well, so what is pertinent?  Your square root argument must not be negative, which restricts your domain

anonymous · Answer

so -5<=x<=5

anonymous · Answer

Next, how does that restrict the domain?  x^2 is always positive, so the biggest the square root part can be is 5, and the smallest is 0, so the range is 0<=y<=5

anonymous · Answer

I don't know what your teacher means by "pertinent information," but you can graph from there.

anonymous · Answer

Square both sides of the equation y=(25-x^2) and rearrange the terms as shown below:
$$y^2 + x^2=5^2$$
I might be wrong but isn't that a circle, centered at the origin with a radius of 5?

anonymous · Answer

but the circle is not a function.  You often can't just square both sides when it is a function.  If the f(x) was really a y, then yes, it is a circle radius 5

anonymous · Answer

What we actually get looks to be the top half of that circle