Find the absolute extrema of the function (if any exist) on each interval. (If an answer does not exist, enter DNE.)

Question

[1, 9)

Answer 1

f(x) = y = sqr(81-x^2) graphically is the top half of a circle with radius = 9, center at the origin (0,0)

range is 0 < y < 9 domain is -9 < x < 9

square both sides to get

y^2 = 81 -x^2

and

x^2 + y^2 = 9^2 which is the full circle. but with the range limited to non-negative numbers, the absolute minimum is zero at both (-9,0) and (9,0), the two x intercepts. The absolute maximum is 9 at the point (0,9) the y intercept.

f(x) is a function, only because the bottom half of the circle is not included. So it passes the vertical line test. It's not a one-to-one function though, as it fails the horizontal line test.