To complete the table and determine which graph corresponds to the function [tex]\( f(x) = 2 \sqrt{x} \)[/tex], let's follow these steps:
1. Compute [tex]\( f(0) \)[/tex]:
[tex]\[
f(0) = 2 \sqrt{0} = 2 \cdot 0 = 0
\][/tex]
2. Compute [tex]\( f(1) \)[/tex]:
[tex]\[
f(1) = 2 \sqrt{1} = 2 \cdot 1 = 2
\][/tex]
3. Compute [tex]\( f(4) \)[/tex]:
[tex]\[
f(4) = 2 \sqrt{4} = 2 \cdot 2 = 4
\][/tex]
Using these calculations, we fill in the table as follows:
[tex]\[
\begin{tabular}{|l|l|}
\hline
$x$ & $f(x)$ \\
\hline
0 & 0 \\
\hline
1 & 2 \\
\hline
4 & 4 \\
\hline
\end{tabular}
\][/tex]
To determine the graph of [tex]\( f(x) = 2 \sqrt{x} \)[/tex], observe the following characteristics:
- The function [tex]\( f(x) = 2 \sqrt{x} \)[/tex] is defined only for [tex]\( x \geq 0 \)[/tex] because the square root of a negative number is not a real number.
- The graph starts at the origin [tex]\((0, 0)\)[/tex].
- As [tex]\( x \)[/tex] increases, [tex]\( f(x) \)[/tex] increases as well, but the rate of increase decreases because the square root function grows slower than a linear function.
Plotting the given points [tex]\((0, 0)\)[/tex], [tex]\((1, 2)\)[/tex], and [tex]\((4, 4)\)[/tex] and considering the shape described, you will be able to match it with the corresponding graph of the function [tex]\( f(x) = 2 \sqrt{x} \)[/tex].
