Consider the given function. Recall that division by zero is not defined. Therefore, the rational function is undefined where The above means that is not included in the domain.
Consider the given function.
Note that we cannot cancel out common factors. Therefore, there are no
holes and if a real number is not included in the domain, there is a vertical asymptote at In this case, we have a vertical asymptote at
Let's pay close attention to the degrees of the numerator and denominator. We see that the degrees of the numerator and denominator are the same. To find the horizontal asymptote, we need to find the quotient between the leading coefficients. Since there is a horizontal asymptote at
The intercepts of the function are the points at which the graph intersects the axes.
Let's make a table of values to graph the given function. Make sure to only use values included in the domain of the function.
Finally, let's plot and connect the points. Do not forget to draw the asymptotes and to plot the intercepts.