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)(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 expression we're given is F multiplied by G evaluated at two. And the graph we're given shows two functions we have F FX in red. This looks like a quadratic function. It opens upwards and has a single root at X equals zero. And then we have the function of X in blue. This looks like a linear function. It's a straight line, right? It has a positive slope. A Y intercept around negative three and an X intercept around 1.5. We're given four answer choices, option A four, option B two, option C eight and option D one. Now we're gonna start by rewriting the expression we were given. So we have F multiplied by G I evaluated at two. Now, we aren't given information about this composite function F multiplied by G. So how are we going to evaluate it at a particular X value? We are given the function F on its own in the graph and the function G on its own in the graph. So recall if we have a function F multiplied by G evaluated at a particular point. In this case two, we can write this as F evaluated at two multiplied by G evaluated at two. So instead of multiplying the functions together and then evaluating them at a particular point, we can evaluate each of the functions F and G at that point on their own and multiply the result together. Now F at two and G at two, we can determine from our graph. So let's go to our graph. We're gonna find X equals two on our graph along the X axis. And we're gonna follow it up to determine the values that we have. So what we hit first is the function G of X. Then we can see that at X equals to G of X is equal to one. OK. So the second part of this G evaluated two is going to be equal to one. And if we keep following that line up, up up, we will find an intersection with the function F of X, then that's gonna be equal to eight. OK. So F at two is equal to eight. So we have eight and we get eight multiplied by one which we know is just equal to eight. And so our original expression F multiplied by G evaluated at two is equal to eight. And the correct answer is therefore option C thanks everyone for watching. I hope this video helped see you in the next one.

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Use the graph to evaluate each expression. See Example 3(a). (ƒg)(0)

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