I have been informed that on March 7th from 6:00am to 6:00pm Central Time Lamar University will be doing some maintenance to replace a faulty UPS component and to do this they will be completely powering down their data center.
Unfortunately, this means that the site will be down during this time. I apologize for any inconvenience this might cause.
Paul
February 18, 2026
Section 1.1 : Review : Functions
22. Find the domain and range of \(M\left( x \right) = 5 - \left| {x + 8} \right|\).
Show SolutionWe’re dealing with an absolute value here and the quantity inside is a line, which we can plug all values of \(x\) into, and so the domain is all real numbers or,
\[{\mbox{Domain : }} - \infty < x < \infty \,\,\,{\rm{or}}\,\,\,\left( { - \infty ,\infty } \right)\]For the range let’s again note that the quantity inside the absolute value is a linear function that will take on all real values. We also know that absolute value functions will never be negative and will only be zero if we take the absolute value of zero. So, we now know that,
\[\left| {x + 8} \right| \ge 0\]However, we are subtracting this from 5 and so we’ll be subtracting a positive or zero number from 5 and so the range is,
\[{\mbox{Range : }}\left( { - \infty ,5} \right]\]