Question

Which of the following functions are discontinuous?1. f(x) =2-2H-2II. f(x) = 42²III. ƒ(x) = z²+3x+22-2=OA. I and III onlyOB. I, II, and IIIOC. I and II onlyOD. II and III only

Answer 1

ANSWER:

B. I, II, and III

STEP-BY-STEP EXPLANATION:

We have the following functions:

$\begin{gathered} f(x)=\frac{x-2}{x-2} \\ \\ f(x)=\frac{x}{4x^2} \\ \\ f(x)=\frac{x-2}{\:x^2+3x+2} \end{gathered}$

All functions are fractional and have an x in the denominator, therefore there will be a value where the denominator is 0 and therefore there would be a discontinuity.

The function is said to be discontinuous if it is not continuous, that is, it presents some point where there is a jump and the graph breaks.

In all the options there will be a discontinuity, therefore the correct answer is B. I, II, and III