Answer
a) Please see the graph.
b) [0, 11.6189] is the domain
c) [0,135] is the range.
d) 4.2426 feet
Work Step by Step
a) The graph was made using graphing software.
b)
$y=135-x^2$
$0 = 135-x^2$
$x^2= 135-x^2+x^2$
$x^2 = 135$
$\sqrt {x^2} = \sqrt {135}$
$x = 11.6189, -11.6189$
We cannot have a negative sidelength, so $x=11.6189$. (We cannot have a negative area, so the maximum value for $x$ was 11.6189.)
c) The range of the function is the possible y-values. Since there cannot be a negative area, the lowest value for the range is 0.
d)
$117 = 135-x^2$
$117-117+x^2 = 135-x^2-117+x^2$
$x^2 = 18$
$\sqrt {x^2} = \sqrt {18}$
$x = 4.2426, -4.2426$
We cannot have a negative sidelength, so $x=4.2426$.
