Use $$ -2,-1,0,1 $$, and 2 for $$ x $$ and find the corresponding values of $$ f(x) $$ for the following exponential function. Then, choose which graph represents the exponential function. $$ f(x)=5^{x} $$

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### Step 1: Compute the function values
For the exponential function $$ f(x)=5^{x} $$, we evaluate it at the given $$ x $$-values:

- When $$ x=-2 $$:
  $$
  f(-2)=5^{-2}=\frac{1}{5^2}=\frac{1}{25}
  $$
  
- When $$ x=-1 $$:
  $$
  f(-1)=5^{-1}=\frac{1}{5}
  $$

- When $$ x=0 $$:
  $$
  f(0)=5^{0}=1
  $$

- When $$ x=1 $$:
  $$
  f(1)=5^{1}=5
  $$

- When $$ x=2 $$:
  $$
  f(2)=5^{2}=25
  $$

### Step 2: Identify the Correct Graph

The graph of an exponential function of the form $$ f(x)=5^{x} $$ should have the following properties:
- It passes through $$ (0,1) $$.
- It is always above the $$ x $$-axis (i.e., $$ f(x) > 0 $$ for all $$ x $$).
- It exhibits rapid growth for positive $$ x $$ and rapid decay (approaching zero) for negative $$ x $$.
- It is strictly increasing on its entire domain.

A graph that correctly shows the points 
$$
(-2,\frac{1}{25}),\ (-1,\frac{1}{5}),\ (0,1),\ (1,5),\ (2,25)
$$
and has the above properties is the one representing $$ f(x)=5^{x} $$.
When $$ x = -2, -1, 0, 1, 2 $$, the corresponding $$ f(x) $$ values for $$ f(x) = 5^{x} $$ are $$ \frac{1}{25}, \frac{1}{5}, 1, 5, 25 $$ respectively. The correct graph should pass through these points and show rapid growth for positive $$ x $$ and rapid decay for negative $$ x $$.

Use , and 2 for and find the corresponding values of for the following exponential function. Then,
choose which graph represents the exponential function.

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Use , and 2 for and find the corresponding values of for the following exponential function. Then, choose which graph represents the exponential function.