Question

use the tables below to find \\((p + q)(2)\\).\\(\

$$\begin{array}{|c|c|}\\hline x&p(x)\\\\\\hline 4&-1\\\\\\hline 2&3\\\\\\hline -3&2\\\\\\hline\\end{array}$$

\\)\\(\

$$\begin{array}{|c|c|}\\hline x&q(x)\\\\\\hline 4&1\\\\\\hline 2&-2\\\\\\hline -3&5\\\\\\hline\\end{array}$$

\\)\\((p + q)(2) = \square\\)

Explanation:

Step1: Recall the definition of \((p + q)(x)\)

By the definition of function addition, \((p + q)(x)=p(x)+q(x)\). So, to find \((p + q)(2)\), we need to find \(p(2)\) and \(q(2)\) first, then add them together.

Step2: Find \(p(2)\) from the first table

Looking at the table for \(p(x)\), when \(x = 2\), the value of \(p(x)\) is \(3\). So, \(p(2)=3\).

Step3: Find \(q(2)\) from the second table

Looking at the table for \(q(x)\), when \(x = 2\), the value of \(q(x)\) is \(- 2\). So, \(q(2)=-2\).

Step4: Calculate \((p + q)(2)\)

Using the formula \((p + q)(2)=p(2)+q(2)\), substitute \(p(2) = 3\) and \(q(2)=-2\) into it. We get \((p + q)(2)=3+(-2)=3 - 2=1\).

Answer:

\(1\)