Use the graphs of f and g to solve Exercises 83–90.

Question

Graph showing functions f(x) in blue and g(x) in orange for Exercises 83-90.

Graph f-g.

Accepted Answer

Hey everyone in this problem we are asked to graph F minus G. Using the graphs shown they were given the graph of Y equals F of X and blue and y equals G of X and red. Alright, so we're doing f minus G. Let's recall that F minus G at x is just equal to f x minus G. X. Okay, so at each point on the graph we just need to find F of X. We need to find G of X which we can do because we've been given their graphs and subtract the two. The easiest way to do this is just to write out a table with all of the values that we are interested in. Um It just helps to keep clean so that we can make sure we're making no mistakes. So our table is going to include X. It's going to include ffx G of X. And then the value we're looking for, f minus G. So we have these four things and I'm just gonna go ahead and on the right hand side I'm going to draw the table again, we're just not gonna have enough room to put all of the values here before we run into these graphs. So we're just going to separate it into two tables so that we can do it where we can still see our graphs. Alright, G, f x and market here, f minus K. So the exact same table is just gonna be a continuation of the X values. Alright, so now the question is, what X values do we use? Okay, well F minus G is going to be defined wherever F. And G are both defined. Okay so we c G. Here starts at negative five but we don't have a corresponding value for negative five because we're not going to include negative five. But they do both have values at negative four. Okay. And onward. So negative four negative three. Negative two, negative 101. We'll stop there. Move over to our other table. Okay and how far do we go? We see that G goes to six and F goes to seven. X. Value of seven. Well if we don't we don't have a G value at seven so we can't find F minus G at seven. So we're gonna stop at X equals six. So we get 2345 and six. Okay so we have all of these X values that we want to find, the value for F minus G. Alright so let's start by finding the values for F of X. We're going to follow this blue curve so that negative four. So negative one negative two, negative three negative four. We follow it up. We see that F this blue line is at five as we value five we go to negative three. The graph stays horizontal so we're still at five and same thing for negative to the graph is horizontal. We're still at five. Okay when we're at negative one this blue curve drops to four at zero. On the Y intercept here. anyone X. Zero. This blue curve is at three and then it stays horizontal at one and two. So we're gonna have three for 13 for X equals two. When X is three. This blue curve is at one When X is four it's that -1. When X is 50. When X is six it's back to positive one. Okay so we're just following that curve and noting the value of the curve of that function F. At all of those X points were interested and we're going to do the same for G. So remember G. This is negative five. We don't have a corresponding F. Value. So we're not including that point. So this point is not getting included in the same thing on the other and this point is not getting included because we don't have a corresponding G value. Okay so the function G at negative four is negative two at at negative three. It's negative or sorry negative yeah negative three. It's negative three, -2. It's negative four and -1. It's down to negative five and then it stays as a horizontal line at zero and one. So it's going to keep that value of negative five at zero and one X equals two. G. Is that negative for X equals one. Is that -3? X equals four. It's at -2. X equals five. Is that -1 and then at X equals six or final X. Value. it drops back down to negative three. Okay so we have all of our values for F. And G. Now we just need to subtract. Okay so five minus negative two. That's going to give us seven. Five minus negative three. That's going to give us eight. Five minus negative four 94 minus negative five 93 minus negative five. Eight and three minus negative five eight. A three minus negative four is 71 minus negative three. It's four one negative one minus negative 210 minus negative one is one and one minus negative three is four. Alright so we have our values of F. N. G. Or f minus G. Sorry let's go ahead and graph I'm going to scroll to the bottom so we have room to graph and I'll just rewrite the f minus G. Values with the X. Values so that we can see. Alright so I'll just rewrite um what we've just calculated so we have X. And we have f minus G. And I'm just gonna rewrite them so that we don't have to go up and down each time but on your page you should be able to see both. Yes we have negative four negative three negative two negative K. And R F minus G values were K. So these are all positive so we can make the negative y axis smaller. We're gonna go from negative four -3 -2 - 123 6 positive six. Okay. And our highest value is nine. Okay so let's go 123-456- nine. Okay. Alright. So plotting this negative four, we have a value of seven. Okay so negative four and seven. We're about here -3 and eight. So we're going up a little bit -2 and nine, A little bit more negative one and 9 Here. zero and 8. Okay. Here and let me you know what let me draw these in blue so we can see when we cross the axis where this dot is. Okay. Zero and eight. Okay. one and 8. Two and seven. Three and four. Four and one five and six and 4. Okay so those are all of our dots for a graph and we can connect them. No like this little messy but. Alright so our graph is gonna look like this. If we go back up to our answer choices, what do we see? We see that the graph that we're looking for is graph. Okay. That matches the graph that we've drawn in all of those values that we found in our table. That's it for this one. Thanks everyone for watching. See you in the next video

Use the graphs of f and g to solve Exercises 83–90.
Graph f-g.

Key Concepts

Function Subtraction

Graphing Functions

Piecewise Functions

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