Is the function $f (x) = 5x – 3$ continuous at $x=-3$

Answer 1

Toolbox:

• If $f$ is a real function on a subset of the real numbers and $c$ a point in the domain of $f$, then $f$ is continous at $c$ if $\lim\limits_{x\to c} f(x) = f(c)$.

Given $f(x) = 5x-3$:

At $x=-3, \; \lim\limits_{x\to -3} f(x) = \lim\limits_{x\to -3} 5x-3 = 5 \times -3 - 3 = -15-3 = -18$

$f(-3) = 5 \times -3 - 3 =-15-3=-18$

Since $\lim\limits_{x\to -3} f(x) = f(-3)$, $f(x)$ is continous at $x=-3$.