Question

f(x) = (x-2)/(x+3)
show that x is continuous at x=1 using difference quotient

Answer 1

The function will be continuous for all values, EXCEPT for -3.
The reason for this is, is because the function has no value at 3.

This discontinuity at x=-3 is given by,\[\lim_{x \rightarrow -3^{}}~f(x) ~~~~~~~~~~\rm does~n ot~exist.\]

Answer 2

I think the professor is asking for us to use the (f(a + h) - f(a)) / h formula