How do you graph #y =1/x^2#?

Question

Savannah Anderson · Accepted Answer

The graph of this function looks like a bell centred around the y axis.

First you must ensure that the denominator is different from zero so you set: #x!=0# The y axis becomes a vertical asymptote of your function; basically the graph of your function will be a curve that gets as near as possible to the y axis without ever crossing it. When #x# gets near zero (but not zero!) the function becomes very big positively (try with #x=0.001# you get #y=1/0.001^2=1,000,000) while when #x# becomes very large (positively or negatively) the function tends to become very small (try with #x=100# you get: #y=1/100^2=0.0001#). So your graph will look like: graph{1/x^2 [-10, 10, -5, 5]} This function is particularly interesting when describing the phenomenon of Resonance in physics!

Ethan Adkins · Answer

undefined To graph the equation y = 1/x^2, you can start by creating a table of values. Choose different values for x, calculate the corresponding y-values using the equation, and plot the points on a coordinate plane. Since the equation involves x^2 in the denominator, it is important to include both positive and negative values of x to accurately represent the graph. Once you have plotted several points, connect them smoothly to form a curve. The graph of y = 1/x^2 will be a hyperbola that opens upwards and downwards, passing through the points (1, 1), (-1, 1), (2, 0.25), (-2, 0.25), (3, 0.111), and so on.