Use the graph to evaluate each expression. See Example 3(a).

Question

(ƒ+g)(2)

Graph showing two functions: a blue parabola y = f(x) opening upward and a red line y = g(x) with positive slope.

Accepted Answer

Hey, everyone in this problem, we're asked to find the value of the expression using the graph given below. Now, the expression we're given is F plus G evaluated at three. The graph we given shows two functions we have F FX in this orangey red color looks like a quadratic that's opening upwards and has a single root at X equals zero. We're also given G of X in blue G of X looks like a linear function. It's a line, it has a Y intercept at negative five and an X intercept around 1.7. We're given four answer choices, option A 13, option B four, option C nine and option D 17. Now we're gonna start by rewriting what we were given. So we have F plus G evaluated at three. Now, we aren't given any information about this function F plus G. So how can we evaluate it at a particular point? Well, we are given information about F on its own and G on its own through our graph, we recall that we can write this as F evaluated at three plus G evaluated at three. So instead of adding the functions together and then evaluating them at the particular X value, we can evaluate each of those functions F and G on their own at three and then add the result together. All right. So we wanna find F at three and G at three. So what we're gonna do is we're gonna go to our graph, we're gonna find X equals three along the X axis. And we're gonna follow that up until we hit our functions. Now we hit the function G of X first at A Y value of four. And so G evaluated at three is going to be equal to four. We can keep following that line up and we find that F evaluated at three is going to be equal to nine. And so our expression becomes nine plus four, which is equal to 13. And so F plus G evaluated at three is equal to 13 and the correct answer corresponds with option A. Thanks everyone for watching. I hope this video helped see you in the next one.

Use the graph to evaluate each expression. See Example 3(a).
(ƒ+g)(2)

Key Concepts

Function Notation and Evaluation

Function Addition (ƒ + g)(x)

Reading Values from a Graph

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