Math Is Fun Forum

smkeddy

Member

Registered: 2014-03-26

Posts: 1

Continuity, specifically for f(x) = 1/x

Right now, I am studying for my Praxis 2 exam to teach high school math. I came across this question on my practice exam:

32. Is the function f(x) = 1/x continuous?

A. No, because you cannot graph the function without lifting your pencil.
B. No, because it is not defined at x = 0.
C. No, because it has no defined minimum or maximum.
D. Yes, because it is defined for all values in its domain, the limit of f(x) exists as x approaches a and the limit equals f(a).

They said the correct answer was D, and I was surprised, I put B. From what I can gather, their logic is that the domain of the function does not include zero, so it is defined at all points in its domain. Is this correct? I`ve found conflicting things online and even in text books.

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: Continuity, specifically for f(x) = 1/x

Yes, it is continuous because 0 is not part of it's domain.

Last edited by ShivamS (2014-03-26 08:18:29)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,134

Re: Continuity, specifically for f(x) = 1/x

hi smkeddy

Welcome to the forum.

I'm not surprised that you get contradictory answers, because there is no absolute authority that determines the definition of mathematical terms.

If you look at Wikipedia:

http://en.wikipedia.org/wiki/Continuous_function

The function f is said to be continuous if it is continuous at every point of its domain.

but also

A function from the set of real numbers to the real numbers can be represented by a graph in the Cartesian plane; such a function is continuous if, roughly speaking, the graph is a single unbroken curve with no "holes" or "jumps".

Wolfram Alpha:

http://www.wolframalpha.com/input/?i=co … lk=4&num=2

A function with no gaps, jumps or undefined points.

If you have been given a definition then that determines how you should respond.  Otherwise the correct answer is "Please define continuous function". 

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob