Algebra - Exponential Functions

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

$The graph of $g\left( x \right) = {{\bf{e}}^{ - x}}$. The blue dashed line is the “base” function $f\left( x \right) = {{\bf{e}}^x}$ and the solid red line is $g\left( x \right)$, which is the graph of $f\left( x \right)$ reflected about the y-axis. The dashed graph increases to the right while the solid graph decreases to the right, and the two cross at $\left( {0,1} \right)$.$