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 6.1 : Exponential Functions
5. Sketch the graph of \(f\left( x \right) = {{\bf{e}}^{x - 3}} + 6\) .
Show SolutionFor this problem all we need to do is recall the Transformations section from a couple of chapters ago. Using the “base” function of \(f\left( x \right) = {{\bf{e}}^x}\) the function for this part can be written as,
\[f\left( x \right) = {{\bf{e}}^{x - 3}} + 6 = f\left( {x - 3} \right) + 6\]Therefore, the graph for this part is just the graph of \(f\left( x \right)\) shifted right by 3 and up by 6.
The graph of this function is shown below. The blue dashed line is the “base” function, \(f\left( x \right)\), and the red solid line is the graph for this part, \(g\left( x \right)\).
