Graphing functions Use the guidelines of this section to make a complete graph of f.
f(x) = x²/(x - 2)

Verified step by step guidance

1. Identify the function f(x) = \frac{x^2}{x - 2} and determine its domain by finding values of x that make the denominator zero.
2. Calculate the vertical asymptote by setting the denominator equal to zero: x - 2 = 0, which gives x = 2.
3. Find the x-intercepts by setting the numerator equal to zero: x^2 = 0, which gives x = 0.
4. Determine the horizontal asymptote by analyzing the degrees of the numerator and denominator; since the degree of the numerator is greater than that of the denominator, there is no horizontal asymptote.
5. Evaluate the behavior of the function as x approaches the vertical asymptote from the left and right to understand the end behavior of the graph.