Question

Match each function with its graph.

$y={\left(\frac{1}{5}\right)}^x$

Short answer

$y={\left(\frac{1}{5}\right)}^x$ is represented by the graph:

Step-by-step solution

Step 1. Given Information.

The function $y={\left(\frac{1}{5}\right)}^x$ is to be matched with its graph among the following:

Step 2. Explanation.

A function is said to be exponential is the variable is in the exponent i.e., of the form $y=a{b}^x+c$

The function has x in the exponent i.e., the degree of the function is a variable.

Hence the function is an exponential function.

And since the base is less than 1, the function is an decreasing function.

Hence the graph is option b.

To verify, when $x=0$:

$\begin{array}{l}y={\left(\frac{1}{5}\right)}^x\\ y={\left(\frac{1}{5}\right)}^0\\ y=1\end{array}$

The graph in options b, passes through $y=1$.

Hence the function is represented by the graph in option b.

Step 3. Conclusion.

Hence, $y={\left(\frac{1}{5}\right)}^x$ is represented by the graph in option a: