Give me the process of sketching graph of rational Functions

Here's the process for sketching the graph of a rational function: Step 1: Find the vertical asymptotes and holes. Set the denominator of the simplified rational function equal to zero and solve for x. These x-values are the vertical asymptotes. If a factor cancels out from both the numerator and denominator, there is a hole at that x-value. Step 2: Find the horizontal or slant (oblique) asymptotes. • If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. • If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is y = (leading coefficient of numerator)/(leading coefficient of denominator). • If the degree of the numerator is one more than the degree of the denominator, there is a slant asymptote. Use polynomial long division to divide the numerator by the denominator; the quotient (ignoring the remainder) is the equation of the slant asymptote, y = mx + b. Step 3: Find the x-intercepts. Set the numerator of the simplified rational function equal to zero and solve for x. These are the points where the graph crosses the x-axis. Step 4: Find the y-intercept. Substitute x = 0 into the function and solve for y. This is the point where the graph crosses the y-axis. Step 5: Test for symmetry. • If f(-x) = f(x), the graph is symmetric about the y-axis. • If f(-x) = -f(x), the graph is symmetric about the origin. Step 6: Plot additional points. Choose x-values in each interval created by the vertical asymptotes and x-intercepts. Evaluate the function at these points to determine the behavior of the graph in those regions. Step 7: Sketch the graph. Draw the asymptotes as dashed lines. Plot the intercepts and any additional points. Connect the points, ensuring the graph approaches the asymptotes without crossing vertical ones. That's 2 down. 3 left today — send the next one.