Question

sketch a graph by completing the table and plotting the points. \\( p(x) = 2sqrt{x} \\) \\( \text{part: } 0 / 2 \\) \\( \text{part 1 of 2} \\) \\( \text{complete the table below.} \\) \\( \

$$\begin{array}{|c|c|} \\hline x & p(x) \\\\ \\hline 0 & \\square \\\\ \\hline 1 & \\square \\\\ \\hline 4 & \\square \\\\ \\hline 9 & \\square \\\\ \\hline 16 & \\square \\\\ \\hline \\end{array}$$

\\)

Explanation:

Step1: Evaluate for \( x = 0 \)

Substitute \( x = 0 \) into \( p(x)=2\sqrt{x} \). We know that \( \sqrt{0} = 0 \), so \( p(0)=2\times\sqrt{0}=2\times0 = 0 \).

Step2: Evaluate for \( x = 1 \)

Substitute \( x = 1 \) into \( p(x)=2\sqrt{x} \). Since \( \sqrt{1}=1 \), then \( p(1)=2\times1 = 2 \).

Step3: Evaluate for \( x = -4 \)

The square root function \( \sqrt{x} \) is only defined for \( x\geq0 \) in the real - number system. So, \( p(-4) \) is undefined (we can note this, but for the table, we can state that there is no real - valued output).

Step4: Evaluate for \( x = 9 \)

Substitute \( x = 9 \) into \( p(x)=2\sqrt{x} \). We have \( \sqrt{9}=3 \), so \( p(9)=2\times3 = 6 \).

Step5: Evaluate for \( x = 16 \)

Substitute \( x = 16 \) into \( p(x)=2\sqrt{x} \). Since \( \sqrt{16}=4 \), then \( p(16)=2\times4 = 8 \).

Answer:

For \( x = 0 \), \( p(x)=0 \); for \( x = 1 \), \( p(x)=2 \); for \( x=-4 \), \( p(x) \) is undefined (no real - valued output); for \( x = 9 \), \( p(x)=6 \); for \( x = 16 \), \( p(x)=8 \)

Filling the table:

\( x \)	\( p(x) \)
\( 1 \)	\( 2 \)
\( -4 \)	Undefined (no real output)
\( 9 \)	\( 6 \)
\( 16 \)	\( 8 \)