Section III: Bonus
Extra credit questions will go up on the blog on Wednesday!
1. What happens as x goes to infinity?
We can’t plug in infinity for x, but we are curious about what happens to a function
when x becomes very, very large (or increases without bound). In other words, we
want to know what the limit of a function is as x goes to infinity. Consider the limit:
1
lim 𝑥. What happens to the function f(x) = 1/x when x goes to infinity?
𝑥→∞
Part 1: plug some enormous numbers into the function and see what happens. What
is f(1000)? f(5000)? f(1000,000)?
Part 2: what are these numbers trending towards? In other words, what is the limit
of 1/x as x goes to infinity?
Part 3: what about the limit as x goes to infinity of 2/x? or 3/x?
2. Vertical Asymptote
Some functions go shooting off to positive or negative infinity at some point in their
domain. The vertical lines they approach when they do this are called asymptotes.
𝑥 3 +7
Part 1: Graph the function 𝑥 2 −4. This function has 2 vertical asymptotes. One of them
is the line x = -2. Graph this line on the same graph.
Part 2: Find the other vertical asymptote of this function.
Part 3: How could you find these asymptotes algebraically?