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 functions f(x) in red and g(x) in blue for evaluating (ƒ-g)(-1).

Accepted Answer

Hey, everyone in this problem, we're asked to find the value of the expression using the graph given below. Now, the graphs were given shows the function F of X in red and a function G of X in blue F FX is a quadratic looking function. It opens upwards and has a single root at X equals zero G FX is a linear function. It's a straight line, OK. It has a positive slope with a Y intercept rate around one. Now, the expression we're given is F minus G evaluated at negative two. We're given four answer choices, option A 11, option B negative three, option C four and option D negative seven. Now we're gonna start by rewriting the expression we were given. So we have F minus G evaluated at negative two. Now this composite function F minus G, we're not given any information about, we're given information in our graph about F on its own and the function G on its own but not of this composite F minus G. We recall composition of functions tells us if we have F minus G evaluated at a particular point. In this case, M negative two, we can write this as F evaluated at negative two minus G, evaluated at negative two. So instead of subtracting the functions first and then evaluating them at that particular point negative two, we can evaluate each function on its own at negative two and subtract the result. So now we need F at negative two and G at negative two, which we can find from the graph we were given. So going to our graphs, we wanna find X equals negative two along the X axis and we're just gonna draw a vertical line until it connects with our functions. Now F FX in red, OK. Intersex this X equals negative two line at four. So the value of F at negative two is equal to four. We can do the same for G. In this case, we're gonna have to follow that line downwards vertically. OK? Because we're in the third quadrant here. And we can see that the function G of X at X equals negative two is negative seven. So we get four minus negative seven. If we have minus a negative value, this is the same as adding. So this is equal to four plus seven, which is equal to 11. OK. So the expression we were asked to evaluate F minus G at negative two is equal to 11. So the correct answer is option A 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). (ƒ-g)(-1)

Key Concepts

Function Evaluation

Graph Interpretation

Function Subtraction

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