Rational Functions

Math 30-1: graphing and analyzing rational functions, asymptotes, and restrictions.

13 questions, free, marked as you go with a worked explanation on every one.

What this covers

For f(x) = 1/(x-4), what value of x is not allowed (the vertical asymptote)?
For f(x) = 1/x, what happens to the graph as x approaches 0?
For f(x) = (x+2)/(x-3), what is the x-intercept?
A horizontal asymptote describes the behavior of a function as:
For f(x) = 3/(x + 2), what value of x gives a vertical asymptote?
What is the y-intercept of f(x) = x/(x - 2)?
For f(x) = (x - 5)/(x + 1), find the x-intercept (where f(x) = 0).
As x → ∞, the function f(x) = (2x + 1)/(x - 3) approaches which value?
A company's average cost per unit is given by C(x) = (2400 + 18x) / x dollars, where x is the number of units made. How many units must the company make for the average cost to fall to $30 per unit?
Evaluate the limit of (x squared minus 9) divided by (x minus 3), as x approaches 3.
For the function f(x) = (x plus 1) divided by (x minus 1), what happens to f(x) as x approaches 1 from the right?
Evaluate the limit of (5x cubed) divided by (2x cubed plus x), as x approaches infinity.
Which statement correctly describes a removable discontinuity in a rational function?