Question

use the graphs of f and g to find (f + g)(2).
(f + g)(2) = \square

Explanation:

Step1: Recall the definition of \((f + g)(x)\)

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

Step2: Find \(f(2)\) from the graph of \(f(x)\)

Looking at the blue graph (which represents \(f(x)\)), when \(x = 2\), we find the corresponding \(y\)-value. From the graph, at \(x = 2\), the \(y\)-value of \(f(x)\) is \(0\) (since the point on \(f(x)\) at \(x = 2\) has a \(y\)-coordinate of \(0\)). So, \(f(2)=0\).

Step3: Find \(g(2)\) from the graph of \(g(x)\)

Looking at the red graph (which represents \(g(x)\)), when \(x = 2\), we find the corresponding \(y\)-value. From the graph, at \(x = 2\), the \(y\)-value of \(g(x)\) is \(0\) (since the point on \(g(x)\) at \(x = 2\) has a \(y\)-coordinate of \(0\)). So, \(g(2)=0\).

Step4: Calculate \((f + g)(2)\)

Using the formula \((f + g)(2)=f(2)+g(2)\), substitute \(f(2) = 0\) and \(g(2)=0\) into it. We get \((f + g)(2)=0 + 0=0\).

Answer:

\(0\)