Determine whether or not the equation defines y as a function of x. if it is a function, find the domain and range. x+y=9, x+y^3=8, x^2+y=16
Solve each equation for y. For the first one,
x + y = 9
y = -x + 9
The graph of this is a line with slope -1 and y-intercept of 9 -- it's clearly a function. There are no restrictions for x (for example, x is not in the denominator or underneath the square root) so the domain is all real numbers. You can also see that the range is all real numbers.
What would be an instance of an equation not being a function? If you take an equation like this and solve for y:
$\displaystyle y^2=x$
$\displaystyle y=\sqrt{x}$ OR
$\displaystyle y=-\sqrt{x}$
You actually get two equations. The graph of $\displaystyle y^2=x$ is a parabola opening to the right; it's not a function (apply the vertical line test).