## Calculus 10th Edition

Published by Brooks Cole

# Chapter P - P.1 - Graphs and Models - Exercises - Page 8: 46

#### 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.

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