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)(1)

Graph showing f(x) as a red parabola and g(x) as a blue line for function composition evaluation.

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 divided by G at five. And the graph we given shows two functions we have F FX drawn in red. OK. This looks like a quadratic function. It's a parabola opening upwards with a single root at X equals zero. And then we have the function G of X drawn in blue. This is a straight line looks like a linear function. It has a Y intercept at negative eight and an X intercept at positive eight. We're given four answer choices, option A 10 divided by three, option B three divided by 10, option C negative 10, divided by three and option D negative three divided by 10. We're gonna start by writing the expression we were given. So we have F divided by G evaluated app. Now we're given information about F on its own and G on its own in our graph. But we aren't given information about F divided by G. So how can we evaluate it at a particular point? Will recall that we can write F divided by G evaluated at five as F, evaluated at five divided by G, evaluated at five. OK. As long as G evaluated at five is not equal to zero. And we don't want to divide by zero. So instead of dividing the functions first and then evaluating at a particular point, we can evaluate each function on its own at that point and then divide the result. All right. So we need to find F F five, We need to find G F five, which we can do from our graph. So we're gonna start and look for X equals five along our X axis. And we're just gonna draw in line up to our function to see where it intersects. And we can see that F of X at X equals five is 10. So in the numerator, we get 10, we're gonna do the same with G of X. In this case, we have to go down because it's below the X axis and we get a value here of negative three. OK. So G evaluated five is negative three. And so we have 10 divided by negative three which we can also write, we can switch where that negative sign is. So we can write this as negative 10 divided by three. OK. So F divided by G evaluated at five is equal to negative 10, divided by three which corresponds with answer choice C. 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)(1)

Key Concepts

Function Evaluation

Graph Interpretation

Function Composition

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