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# Examine the following functions for continuity. $f(x) = x-5$

This is a multipart question answered separately on Clay6

• 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 $\lim\limits_{x\to c} f(x) = f(c)$.
• Every polynomial function $f(x)$ is continous.
Given that every polynomial function is continuous, and $f(x)$ a polynomial function, it is continuous.