This Student Video is about finding all the pieces of a rational function and graphing all the parts. In order to, graph our rational functions we first need to sketch our asymptotes (horizontal or slant[never both] and vertical[if we have one]). Then, we need to plot any holes with open circles. Next, we need to plot the x and y intercepts whether if it is many or one. Finally, we use the vertical asymptote to divide the graph into sections and find at least three points in each section to help graph. To find the horizontal asymptote if any, you compare the degrees of the numerator and denominator and if bigger on bottom:y=0, same degree:asymptote is the ratio of the coefficients, and bigger degree on top: no horizontal asymptote. Slant asymptotes only exists if the numerator's degree is one bigger than the denominator and you use long division to divide the rational function and everything except the remainder is the equation of the slant asymptote. To find vertical asymptotes you factor both the top and bottom f the rational function and cross off any common factors. Then, you set the denominator equal to zero and solve.
The viewer needs to pay attention to the cancellation of common factors will give you holes and holes are plotted with open circles. Also, they need to remember that domain is both vertical asymptote and holes. Finally, the viewer needs to pay attention for the number of x-intercepts. X-intercepts can have more than one or none, but y-intercepts is only one or none.
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