I need help on this math question, someone!?

Question

http://i24.tinypic.com/24gvn0p.jpg

I need to learn how to solve the problem above. And I really want to learn how to do it, not just the answer. Can someone please help explain it to me?

Answer 1

Note that the graph is unbroken. In calculus we
say that f(x) is continuous.
Note that f(x) = 0 for x = -3 and x = 3 for x = 0
and that f(x) is increasing on [-3,0].
That means that the graph starts out
below the line y = 2 and ends up above it
on [-3,0]. By a theorem from calculus called
the intermediate value theorem,
it must cross the line y = 2 once on that interval.
Now let's look at the interval [0,6].
Suppose the graph reaches it's low point
at x = a. The function is decreasing on [0,a]
and it starts out above the line y = 2 and ends
up below it. So it crosses the line y = 2 once
on [0,a].
Finally, look at [a,6]. The graph is increasing
on [a,6], starts out below y = 2 and ends up above it.
So it crosses the line y = 2 once on [a,6].
All in all it crosses the line y = 2 3 times
on [-3,6].
Essential thing to remember:
If a graph is unbroken, starts out below
the line y = k and ends up above it, it
must cross the line y = k somewhere in between.

Answer 2

you need to find out where f(x) = 2, i.e. where the function (curve) crosses the line y=2. You know the point where it crosses the y-axis is (0,3), and the point line y=2 falls just below this point. If you drew it, you would see the function crosses y=2, 3 times. If you wanted to be accurate, you would need to talk about increasing and decreasing function between certain points.

Answer 3

three as y = 2 intersects the graph at 3 points.

Answer 4

Tim said C