Graphing functions Use the guidelines of this section to make a complete graph of f.
f(x) = 3x/(x² - 1)

Verified step by step guidance

1. Identify the function f(x) = 3x/(x² - 1) and determine its domain by finding values of x that make the denominator zero.
2. Calculate the vertical asymptotes by setting the denominator x² - 1 equal to zero and solving for x.
3. Find the x-intercepts by setting the numerator 3x equal to zero and solving for x.
4. Determine the horizontal asymptote by analyzing the behavior of f(x) as x approaches infinity or negative infinity.
5. Plot key points, asymptotes, and intercepts on the graph, and sketch the curve to represent the function's behavior.