Rational functions often have x values that make them undefined. However, some of these create “holes” in the graph and others create asymptotes. Refer to
the given functions:
1) Fill in the y-values for x-values in the attached chart below:
Week 6 Chart
x y=f(x) y=g(x) y=h(x)
1.9
1.99
1.999
1.9999
2
2.0001
2.001
2.01
2.1
2) Which graphs would you say have a hole at the x-value of 2 and which have an asymptote at the x-value of 2? Explain your decisions.
3) Factor the numerator and denominators of these functions. What conclusions can you make about those functions that create holes and those that create asymptotes?
4) Create your own rational function with a hole and your own rational function with an asymptote.
