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

Question

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

(ƒ+g)(0)

Graph showing two functions: a blue linear function increasing and a red downward parabola, with labeled axes.

Accepted Answer

Hey, everyone in this problem, we're asked to find the value of the expression using the graph given below. Now, the graph we given shows two functions F FX is in red and G FX is in blue, F FX looks like a quadratic function. It's opening upwards and has a single root at X equals zero. G FX is a linear function. It's a straight line, it has an X intercept around X equals negative two and A Y intercept around X equals or sorry around Y equals nine. The expression we're given is F plus G evaluated at five. We have four answer traces. Option A 29 option B 54 option C option D 49 we're gonna start by rewriting the expression we were given. So we have F plus G evaluated at five. Now, we aren't given any information about this composite function F plus G. OK. In the graph, we're given information about the function F on its own and the function G on its own recall information about our composite function. If we have F plus G evaluated at five, we can write this as F evaluated at five plus G evaluated at Y. So instead of adding the two functions F plus G together first and then evaluating that at a particular X value five, we can take each function, evaluate it at five and then add the result together. So F at five, we can find this using our graph. We're gonna go to our graph, we're gonna find X equals five along our X axis. We're just gonna go up from there until we reach our curve of F of X. And that is going to intersect an F M X equals 25. OK. So the value of F F five is equal to 25 and we can do the same for G. OK? So G is a little bit above. In this case, we're gonna keep following that line upwards and we get to an intersection of 29. So G evaluated at five is equal to 29. OK? So now we just have to do 25 plus 29. This gives us a value of 54. And so our original expression F plus G evaluated at five is equal to 54. The correct answer is therefore option B, that's it for this one. Thanks everyone for watching. I hope this video helped.

Use the graph to evaluate each expression. See Example 3(a).
(ƒ+g)(0)

Key Concepts

Function Evaluation

Function Addition

Reading Values from a Graph

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