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Section 6.1 : Exponential Functions

5. Sketch the graph of \(f\left( x \right) = {{\bf{e}}^{x - 3}} + 6\) .

Show Solution

For 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, \(g\left( x \right)\).