You are here:

Question
I am practicing for my ACT exams, but I cannot get this question right on the practice test. First I thought H, and then F, but I am having trouble with it.

Suppose the following:

f(x)=(3x(x-1))/(x^2-3x+2), for x cannot equal 1 or 2.
f(1)=-3
f(2)=4

This means that f(x) is continuous at which of the following:
F) except at x=1
G) except at x=2
H) except at x=1 or 2
I) except at x=0, 1 or 2
J) at each real number

f(x) is continuous at x=1 because
1 is part of the domain
f(1) = -3
limit of 3x(x-1)/(x˛-3x+2) as x approaches 1 = -3 = f(1)

Limit of 3x(x-1)/(x˛-3x+2) as x approaches 2 from the left is -∞.
The limit of 3x(x-1)/(x˛-3x+2) as x approaches 2 from the right is ∞.
However, f(2) ≠ -∞ or ∞. The function is discontinuous at x=2.
=====
Sorry, I must retract this answer—may have made a mistake regarding the limit as the function approaches 2.
Will check my work and update.

Volunteer

#### Janet Yang

##### Expertise

I can answer questions in Algebra, Basic Math, Calculus, Differential Equations, Geometry, Number Theory, and Word Problems. I would not feel comfortable answering questions in Probability and Statistics or Topology because I have not studied these in depth.

##### Experience

I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

Publications
Co-author of An Outline of Scientific Writing: For Researchers With English as a Foreign Language

Education/Credentials
I have a Bachelor's degree in Applied Mathematics from the University of California at Berkeley.

Past/Present Clients
George White Elementary School. Homework Help program at the Ridgewood Public Library, Ridgewood, NJ. Individual students.