The function I am trying to graph is $y = \sqrt{8-2x^2}$. When I graph this online there's no problem, but my graphing calculator shows a graph that does not intersect with the y-axis. Shouldn't the graph intersect with the y-axis at points $(2,0)$ and $(-2,0)$?
Here's the image of the function graphed by my ti-89.
Please do help... I've been spending some time trying to figure out the problem but never figured out why the function is graphed like that.
This is just a numerical issue. Your calculator has an $x$-value for every column of pixels, an calculates the corresponding $y$ value. Only at very specific zoom settings will $x=2$ be in the $x$-values that your calculator is using.
What you see is one point with $x$ slightly smaller than $2$, at which your calculator happily plots the function, and one point with $x$ slightly greater than $2$, at which the result is imaginary and your calculator doesn't plot it.
More sophisticated plotting tools can be cleverer in such cases, maybe by subdividing the interval to better approximate the point at which $y$ stops being real, or maybe by doing the required algebra.