To determine the first step Chelsea takes when graphing the function [tex]\( f(x) = 20 \left( \frac{1}{4} \right)^x \)[/tex], we need to find the initial value of the function.
The initial value of the function refers to the value of [tex]\( f(x) \)[/tex] when [tex]\( x = 0 \)[/tex]. So, we'll substitute [tex]\( x = 0 \)[/tex] into the function to find [tex]\( f(0) \)[/tex].
Evaluating:
[tex]\[
f(0) = 20 \left( \frac{1}{4} \right)^0
\][/tex]
Anything raised to the power of 0 is 1. Therefore:
[tex]\[
\left( \frac{1}{4} \right)^0 = 1
\][/tex]
So, we have:
[tex]\[
f(0) = 20 \cdot 1 = 20
\][/tex]
Thus, the initial value of the function [tex]\( f(x) = 20 \left( \frac{1}{4} \right)^x \)[/tex] is 20. Chelsea would start by plotting the point (0, 20) on the graph.
Hence, the graph that represents her first step is the one which has a point at (0, 20).
