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Using polynomial division, divide the numerator by the denominator to determine the line of the slant asymptote. To find x and y intercepts, set each variable equal to zero and solve in turn. Based on information gained so far, select x values and determine y values to create a chart of points to plot.
Finding Horizontal Asymptotes of Rational Functions
If both polynomials are the same degree, divide the coefficients of the highest degree terms. ...
If the polynomial in the numerator is a lower degree than the denominator, the x-axis (y = 0) is the horizontal asymptote.
To find the y-intercept(s) (the point where the graph crosses the y-axis), substitute in 0 for x and solve for y or f(x). To find the x-intercept(s) (the point where the graph crosses the x-axis â€“ also known as zeros), substitute in 0 for y and solve for x. Examples: Find the intercepts of the function given.