Use a graphing utility to construct a table of values for the function.Round your answer to two decimal places. $$f ( x ) = \left( \frac { 1 } { 5 } \right) ^ { x }$$
A) $$\begin{array} { | c | c | c | c | c | c | }
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & & & & & \
f ( x ) & 25.00 & - 5.00 & 1.00 & 0.20 & 0.04 \
\hline
\end{array}$$
B) $$\begin{array} { | c | c | c | c | c | c | }
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 25.00 & 5.00 & - 1.00 & 0.20 & 0.04 \
\hline
\end{array}$$
C) $$\begin{array} { | c | c | c | c | c | c | }
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & & & & & \
f ( x ) & - 25.00 & 5.00 & 1.00 & 0.20 & 0.04 \
\hline
\end{array}$$
D) $$\begin{array} { | c | c | c | c | c | c | }
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 25.00 & 5.00 & 1.00 & 0.20 & 0.04 \
\hline
\end{array}$$
E) $$\begin{array} { | c | c | c | c | c | c | }
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 25.00 & 5.00 & 1.00 & - 0.20 & - 0.04 \
\hline
\end{array}$$

Question

Use a graphing utility to construct a table of values for the function.Round your answer to two decimal places.​ $$f ( x ) = \left( \frac { 1 } { 5 } \right) ^ { x }$$ ​
A) $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & & & & & \
f ( x ) & 25.00 & - 5.00 & 1.00 & 0.20 & 0.04 \
\hline
\end{array}$$
B) $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 25.00 & 5.00 & - 1.00 & 0.20 & 0.04 \
\hline
\end{array}$$
C) $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline & & & & & \
f ( x ) & - 25.00 & 5.00 & 1.00 & 0.20 & 0.04 \
\hline
\end{array}$$
D) $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 25.00 & 5.00 & 1.00 & 0.20 & 0.04 \
\hline
\end{array}$$
E) $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline f ( x ) & 25.00 & 5.00 & 1.00 & - 0.20 & - 0.04 \
\hline
\end{array}$$

Quizplus · Accepted Answer

The function $f(x) = \left(\frac{1}{5}\right)^x$ represents exponential decay. When $x$ is negative, the function value increases because the base $\frac{1}{5}$ is raised to a negative exponent, effectively flipping the fraction to $5^{|x|}$. For $x=0$, any number to the power of 0 is 1. As $x$ becomes positive, the function value decreases because $\frac{1}{5}$ to any positive power is a fraction less than 1. The values in option D correctly follow this pattern.

Use a Graphing Utility to Construct a Table of Values f(x)=(15)xf ( x ) = \left( \frac { 1 } { 5 } \right) ^ { x }f(x)=(51​)x

Use a Graphing Utility to Construct a Table of Values $f ( x ) = \left( \frac { 1 } { 5 } \right) ^ { x }$