The document provides step-by-step instructions for graphing rational functions. It explains that rational functions are fractions of polynomials, and defines key features like domains, zeros, vertical and horizontal asymptotes. Examples are given to demonstrate identifying these features and graphing the rational function based on them. Steps include finding intercepts, asymptotes, determining where the graph lies relative to the x-axis, and combining these elements to graph the full function.

3. Examples: Because rational functions are expressed in the form of a fraction, the denominator of a rational function cannot be zero, since division by zero is not defined.

5. Graphing Rational Functions Step 1: Identify zeros (x-intercepts) of the function. The zeros of this function are found by setting y to 0 and solving for x: We see that when we do this, we find that the numerator determines our zeros. In this case, our zero is found by solving x −1=0, so x = 1 is our zero. Step 2: Identify our vertical asymptotes. We know that this function is undefined when the denominator is 0. So, let us find for which x-values the denominator is equal to zero. Our graph will contain vertical asymptotes at these x-values. We want to solve the equation 2 x 2 +7x+3=0.

6. So, our graph contains two vertical asymptotes, which represent values of x that our function does not contain in its domain. Our graph will tend towards these x-values, but will never pass through them.

16. Start putting it together When we put the asymptotes, intercepts, and hole on the graph it’s easy to see where the graph goes…