Rational functions

Question

What is the point of discontinuity of this function and why?

(2x)/(x^2 +2x)

 

The answer was (0,1)

Answer 1

The domain of the function is {x| x ≠ 0, x ≠ -2}

 

The function is discontinuous at those x-values.

 

At x = -2, the function is undefined and so no 'point' of discontinuity.

 

Factoring and simplifying yields 2/(x+2). The original function and its simplification still have the domain restriction that

x ≠ 0, but the simplified form computes to 1 if x = 0.

 

In the graph, this is known as a 'missing point' discontinuity - since (0,1) is valid for the simplification, though not as a defined point in the function

 

Answer 2

f(x) = 2x / (x² + 2x)

f(x) = 2x / x(x + 2)

 

X may not be a value that makes the denominator zero.

 

x ∉ {0, -2}