Question 316831
{{{ y = 1 - x^2 }}}
Domain = {-1, 0, 1} 
{{{y(-1)=1-x^2=1-1=0}}}
{{{y(0)=1-0=1}}}
{{{y(1)=1-1=0}}}
Range=(0,1)
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{{{y = 4x - x^2}}}
Domain = {-1, -2, 0} 
{{{y(-1) = 4(-1) - 1=-5}}}
{{{y(-1) = 4(-2) - 4=-12}}}
{{{y(0) = 4(0) - 0=0}}}
Range=(0,-5,-12)
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{{{y = t^2 + t - 2}}}
Domain = {-2, -1, 0, 1} 
{{{y(-2) = 4-2-2=0}}}
{{{y(-1) = 1-1-2=-2}}}
{{{y(0) = 0-0-2=-2}}}
Range=(0,-2)
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{{{y = z^2 - 3z}}}
Domain = {-1, 0, 1, 2}
{{{y(-1) = 1 - 3(-1)=1+3=4}}}
 {{{y(0) = 0 - 0 = 0}}}
{{{y(1) = 1 - 3 = -2}}}
{{{y(2) = 4 - 6= -2}}}
Range=(4,0,-2)
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{{{y = 2/ (x + 3)}}}
The domain is all x for which the function makes sense. 
For this function, all x are allowed except for the x which makes the denominator equal to zero because division by zero is undefined.
Find the value when the denominator equals zero.
{{{x+3=0}}}
{{{x=-3}}}
So then the domain is, in interval notation,
({{{-infinity}}},{{{-3}}})U({{{-3}}},{{{infinity}}})