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### Section 6-1 : Exponential Functions

4. Sketch the graph of $$f\left( x \right) = {{\bf{e}}^{ - x}}$$ .

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,

$g\left( x \right) = {{\bf{e}}^{ - x}} = f\left( { - x} \right)$

Therefore, the graph for this part is just the graph of $$f\left( x \right)$$ reflected about the $$y$$-axis.

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