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

Question

Use the graph to evaluate each expression. See Example 3(a). (ƒg)(1)

Graph showing functions f(x) in red and g(x) in blue for evaluating (ƒg)(1).

Accepted Answer

Hey, everyone in this problem, we're asked to find the value of the expression using the graph given below the expression we're given is F multiplied by G evaluated at four. Now, the graph given shows two separate functions. We have F FX in red and we have G FX in blue. Now, F of X looks like a quadratic function. It has one root X equals zero. OK. And it opens upwards G FX is a line, OK? It has a positive slope with an X intercept around negative one and A Y intercept around Y equal five. We're giving four answer choices, option A 16, option B 21 option C 336 and option D 37. Now let's start by writing what we were given. So we have F multiplied by G evaluated at four. Now, we aren't given information about this function F multiplied by G. We're given information in the graph about F on its own and about G on its own. But recall, OK. Our composition of functions tells us that if we have the function F multiplied by G evaluated at four, this is equivalent to writing the function F evaluated at four, multiplied by the function G evaluated at four. OK. So instead of multiplying the functions first and then evaluating at a particular point, we can evaluate each function on its own at that point and multiply the result together. So let's use our graph to find these values. OK. We have F evaluated at four. So we're gonna look at our graph of F FX in red, we're gonna go to an X value of four. We're just gonna go up from there until we see where that red curve intersex. Then that is going to intersect at F F four equals 16. Yes, we have a value of 16. We're gonna do the same for G. So we're gonna keep going up till we hit that balloon curve and that is gonna happen at 21. And so our value of the function G at X equals four is 21. So we have 16, multiplied by 21 which equals 336. So F multiplied by G evaluated at four is equal to 336. OK. So the correct answer corresponds with option C. 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). (ƒg)(1)

Key Concepts

Function Composition

Evaluating Functions from Graphs

Interpreting Graphs

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