# How do you graph f(x)=5^x?

Aug 10, 2015

Find the intercepts and asymptotes, plot a few points, and then sketch the graph.

#### Explanation:

$f \left(x\right) = {5}^{x}$

Step 1. Find the domain and range.

$f \left(x\right)$ is defined for all real values of $x$, so the domain is the set of all real numbers.

${5}^{x} > 0$, so the range is $f \left(x\right) > 0$

Step 2. Find the $y$-intercept.

Let $x = 0$.

$y = {5}^{0} = 1$

The $y$-intercept is at ($0 , 1$).

Step 3. Find the $x$-intercept.

There is no $x$-intercept, because the range is $f \left(x\right) > 0$.

Step 4. Find the horizontal asymptote.

As $x$ decreases without bound, ${5}^{x}$ approaches $0$.

The horizontal asymptote is at $y = 0$.

Step 5. Calculate some extra points.

We have one point: $f \left(0\right) = 1$.

$f \left(1\right) = {5}^{1} = 5$

$f \left(- 1\right) = {5}^{- 1} = \frac{1}{5}$

Step 6. Plot the axes and your three points. Step 7. Complete the graph with a smooth curve through the three points. 