Question

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

$x$	$p(x)$
$2$	$3$
$-3$	$2$

$x$	$q(x)$
$2$	$-2$
$-3$	$5$

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

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 table of \(p(x)\)

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

Step3: Find \(q(2)\) from the table of \(q(x)\)

Looking at the table for \(q(x)\), when \(x = 2\), the corresponding 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: \((p + q)(2)=3+(-2)=3 - 2=1\).

Answer:

\(1\)