Finding (f+g)(8) on a Graph: A Simple Animation Guide

Welcome to understanding function addition! Today we'll explore how to add two functions together.Let's start by looking at our coordinate plane where we'll graph two functions.Here's our first function f of x, shown in blue.And here's our second function g of x, shown in red.When we write f plus g of eight, we're looking to add these functions at x equals eight.Let's focus on x equals eight. We'll draw a vertical line here to help us locate the important points.Notice how this line intersects both functions. These intersection points represent f of eight and g of eight.Now that we have our vertical line at x equals 8, let's find where it intersects each function.Let's start with function f. At x equals 8, f of 8 equals 2.For function g, when x equals 8, g of 8 equals negative 2.These two values, f of 8 equals 2 and g of 8 equals negative 2, are the individual outputs we need to add together.Remember these values, as we'll use them in our next step to find their sum.Now that we have located both f of 8 and g of 8, let's add these values together.To find f plus g of 8, we add the individual values: f of 8, which is 5, plus g of 8, which is 3.We can visualize this addition on our y-axis by starting at f of 8 and adding g of 8 to it.This gives us our final answer: f plus g of 8 equals 8.This point represents the value of our combined function f plus g at x equals 8.