Continuity on functions

Question

Where is  discontinuous?

Options:

1. f(x) is continuous everywhere
2. 1
3. 1, 4
4. 4

Answer 1

If the denominator of a fraction is zero, then the value becomes undefined. (1/0 = infiniity)

So, simply write x² - 5x + 4 = 0 and solve for x

To visualize things like this, use a graphing calculator or online graphing tool (eg DESMOS)

Answer 2

f(x) is discontinuous at x=4 and undefined (and therefore discontinuous) at x=1.