Question

2: If \(f\) is continuous on \(\left( { - \infty ,\infty } \right)\), what can you say about its

graph?

Short answer

The graph of the function has no break, no hole, and no vertical asymptotes

Step-by-step solution

Continuity of a function

A function\(f\)is said to be continuous at a number\(a\)if it satisfies the following conditions:

1.\(f\left( a \right)\)is defined

2.\(\mathop {{\rm{lim}}}\limits_{x \to a} f\left( x \right)\)exists

3. \(\mathop {{\rm{lim}}}\limits_{x \to a} f\left( x \right) = f\left( a \right)\).

Observe the given condition

It is given that function \(f\) is continuous at the number \(\left( { - \infty ,\infty } \right)\). This implies that the function is defined on the given interval.

As the function is continuous in the interval, then the function's graph has no break, and the graph has no hole or vertical asymptotes.