Answer
y=$\sqrt (25-x^{2}$)
x-intercepts at (5,0) and (-5.0)
y-intercept at (0,5)
Work Step by Step
Find Intercepts:
x-int
0=$\sqrt (25-x^{2}$)
x=5,-5
x-intercepts at (5,0) and (-5.0)
y-int
y=$\sqrt (25-0^{2}$)
y=5,-5
y-intercept at (0,5)
Find Symmetry:
Substitute -x for x. If equation is equivalent, graph is symmetric to y-axis.
y=$\sqrt (25-(-x)^{2}$)
y=$\sqrt (25-x^{2}$)
Equations are equivalent, so function is symmetric to y-axis.
Substitute -y for y. If equation is equivalent, graph is symmetric to x-axis.
(-y)=$\sqrt (25-x^{2}$)
y=-$\sqrt (25-x^{2}$)
Equations are not equivalent, so not symmetric to x-axis.
Substitute -y for y and -x for x. If equation is equivalent, graph is symmetric to origin.
(-y)=$\sqrt (25-(-x)^{2}$)
y=-$\sqrt (25-x^{2}$)
Equations are not equivalent, so not symmetric to origin.
