SOLUTION: Help me with my assignment. Please, Find the domain and range for the function defined by f(x)= x^2+2 for -2<x≤1.

The domain is given as {x|-2 < x ≤ 1}, which in interval notation is (-2,1]

For the range, let's graph it:



Now we'll cut it off past the domain on each side, and indicate the
domain at the bottom (in green), and the range on the right of the
graph (also in green).



As we can see, the range goes from the lowest point, which is the vertex of
the parabola, to the highest point of the graph.

The x-coordinate of the vertex of a parabola is found with the formula

 for the equation , So for

, a=1, b=0, so the x-coordinate of the vertex is
 and the y-coordinate is 02+2 = 2.

So the vertex is the point (0,2)

The graph does NOT include the point (-2,6), but it DOES include the point
(1,3).  The graph DOES include the vertex (0,2).

So the range is from the y-coordinate of the vertex (0,2), which it DOES
include, to the y-coordinate of the top point (-2,6), which it DOES NOT
include.

So the range is [2,6).

Edwin