Question 1182489


Find any intercepts and test
for symmetry. Then sketch the graph of the equation.

1. {{{y = 1 -abs(x)}}}

x-intercepts:
{{{0 = 1 -abs(x)}}}
{{{abs(x) = 1 }}}=>{{{x=1}}} or {{{x=-1}}}

y-intercepts:
{{{y = 1 -abs(0)}}}
{{{y = 1 }}}

Replace x with (-x). Simplfy the equation. If the resulting equation is equivalent to the original equation then the graph is symmetrical about the y-axis.

 {{{y = 1 -abs(-x)}}} since {{{abs(x) = abs(-x)}}}, the graph is symmetrical about the y-axis 


{{{ graph( 600, 600, -10, 10, -10, 10, 1 -abs(x)) }}}



2. {{{x = y^2 - 5}}}

x-intercepts:

{{{x = 0^2 - 5}}}
{{{x =  - 5}}}

y-intercepts:
{{{0 = y^2 - 5}}}
{{{5= y^2 }}}
{{{y=sqrt(5)}}} or {{{y=-sqrt(5)}}}->exact answer

approximate answer:

{{{y=2.24}}} or {{{y=2.24}}}



Replace y with -y in the equation
{{{x = (-y)^2 - 5}}}=>{{{x = y^2 - 5}}}
Since replacing y with -y gives the same equation, {{{x = y^2 - 5}}} is symmetric with respect to the x-axis.


{{{ graph( 600, 600, -10, 10, -10, 10, sqrt(x+5),-sqrt(x+5)) }}}