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

Question

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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 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.

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

Function Composition

Reading Values from a Graph

Understanding Quadratic and Linear Functions

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