Question 43466
a. h(x) = x+3 / x-5
{{{y = (x + 3)/(x - 5)}}}
The denominator can not be equal to five because anything divided by zero is undefined.
Domain: {{{x<5}}} or {{{x>5}}}
<====(5)====>
{{{ graph( 600, 600, -10, 10, -10, 10, (x + 3)/(x - 5) ) }}}
b. SQRT x^2+7
{{{y = sqrt(x^2 + 7)}}}
You can not take the square root of a negative number.
{{{x^2 + 7 >= 0}}}
{{{x^2 >= -7}}}
{{{x >= sqrt(-7)}}} and {{{x >= -sqrt(-7)}}}
{{{x >= i*sqrt(7)}}} and {{{x >= -i*sqrt(7)}}}
Domain: all reals
{{{ graph( 600, 600, -10, 10, -10, 10, sqrt(x^2 + 7) ) }}}