Range of a Piecewise Function

David Miller
David Miller
• • 2 min read

$\Begingroup$ Apologies, This Is a Simple Question but I Seem to Have Some Sort of Brain Freeze. I'm Looking for the Range of This Piecewise Function...

Range of a Piecewise Function
$\begingroup$

Apologies, this is a simple question but I seem to have some sort of brain freeze. I'm looking for the range of this piecewise function:

$$f(x)=\begin{cases}x+9&\text{ if } x<-3\\ -2x&\text{ if }-3\leq x\leq 3\\ -6&\text{ if }x>3\end{cases} $$

The domain is $\mathbb{R}$ and is the range $[-6,6]$ or $(-\infty, -6]$?

Thanks

$\endgroup$
6

1 Answer

$\begingroup$

If $x<-3$ we get $f(x)<6$ and $f(-3)= -2(-3) =6$ so $(-\infty,6]\subseteq Range(f)$.

We get nothing new from other parts of function. So $Range(f)= (-\infty,6]$ since it is continuous on $(-\infty ,-3]$.

$\endgroup$
1

Must Read

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

David Miller

David Miller

Executive Financial & Market Analyst
Twitter Linkedin Medium

David Miller brings 15 years of experience in global economics, personal finance strategy, and market dynamics. He specializes in turning complex economic trends into actionable insights for everyday readers.

Share this article
Twitter Facebook Pinterest