Learning Resources

Investigation3: Discontinuities and Vertical Asymptotes

Step A

 Each graph has a vertical asymptote. Hence, the graph is discontinuous at that x-value. This is because, as x approaches the value at which the function is undefined, the value of the denominator tends to zero while the value of the numerator does not. Therefore, as x approaches the value that corresponds to the discontinuity, the function becomes very large in absolute value.

Note: If you trace along the graph you get some advance warning of the discontinuity because the value of the function sharply increases or decreases close to the discontinuity.