how to draw that f(x) does not equal 4 for all x in [1,3]

Question

This graph is defined at [1,3] but is not continuous at x=2. 

Answer 1

x=2 must be either a vertical asymptote or a discontinuity.

 

 

If vertical asymptote, you will draw your graph getting closer to x=2 but never touching x=2.

 

If discontinuity, you will draw your graph with an open circle at x=2.  This is what we call the limit of f(x) as x approaches 2.