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

Question

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

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.

Struggling with College Algebra?

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

Watch next

Function Composition practice set