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how would I graph y= 1/(x^2-4) using the graph y=x^2-4. can you explain all the steps to do this?

you can start by noting that there are vertical asymptotes at x = -2 and x=2

because division by zero is undefined.

Review rational functions to see about horizontal asymptotes and other characteristics.

Did you know?

Did you know that you can graph the equation y=1/(x^2-4) using the graph of y=x^2-4? Here's how: First, start by plotting the graph of y=x^2-4. Next, determine the domain of the function y=1/(x^2-4), which is all the x-values where the denominator x^2-4 is not equal to zero (since division by zero is undefined). In this case, the denominator is zero when x=2 and x=-2, so the domain is all real numbers except x=2 and x=-2. Now, plot points on the graph of y=x^2-4 for various x-values excluding x=2 and x=-2. Once you have these points, simply plot their reciprocals to get the graph of y=1/(x^2-4). Remember to approach positive and negative infinity on the graph as the x-values get closer to 2 and -2 respectively, since the denominator gets close to zero in these cases.