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 college algebra exercises.

Graph f+g.

Accepted Answer

everyone in this problem? We are asked to graph F plus G. Using the graph shown. And were given the graph of Y equals F of X in blue and white equals G of X in red. All right. So, let's think about what F plus G is. Okay, if we have F plus G of X. Oops, recall that This is equal to F of X plus G of X. Okay. So in order to figure out the values of F plus G, what we need to do is figure out the value of F. The value of G and add them together, which we can do because we have the graph for each of them. All right. So, when we're doing something like this from a graph and we're asked to graph it, the easiest thing to do is just to draw a table. Right. All of the values were interested in. And it's just a nice neat way to keep the information. Okay, so we have X. We have F of X. We have G. F X. And then we have F plus G that we're interested in. So, draw these on the table. And I'm just gonna do a dotted line here. And I'm going to do a second table on the right hand side. It's gonna be the exact same. We're just gonna run out of room before we hit these graphs for our rose. So, we're just gonna do a second one here. So, we have room for all of the values we're interested in X. F of X. G, F X and F plus G. Just like before. Alright. Okay. So now we need to figure out what X. Values were interested. Okay now let's recall that the domain of F plus G. It's gonna be the intersection of the domain of F. The domain of G. Okay. So what we wanna do is we want to find all of the points that kind of overlap. Okay. So if we look at the graph of F, it starts at 1234. Okay. So it starts at X equals negative four. The graph of G. On the left hand side starts at X equals negative five. Okay, but we don't have a value for X at negative earth for F. At negative five. Sorry? So we can't find F plus G. Okay, so we're going to ignore this point on G. Um because it's not going to contribute to F plus G. And similarly on the right hand side we have a value for F. At X equals seven, but we don't have a value for G. At X equals seven. Okay, So we can't find F plus G. There because there is no value for G. And so we're gonna ignore this point as well. Okay, so we get rid of those two points and now we have from negative four to positive six. Okay, so we're gonna have negative four -3 - - and six. Okay. All right, so let's just start with F. We're just gonna trace along that blue curve and figure out which values we have. Okay so we're going to do them in blue because the graph is in blue. Okay? So at -4. The function f is at positive five. It keeps a horizontal line. So at negative three it's still at positive five. And at negative two. Again that horizontal line is still at five. Okay. A negative one it drops down to four and at zero or y intercept is at three. Moving into the positive X values at X equals one. We have a horizontal line. Okay? So we're still at three and same for X equals to this horizontal line continues. So we have three for one and three for X equals two. When X is equal to three the function F drops down to one X equals to four. What's that negative one? At X equals to five. It's at zero and at X equals six. It's back up to positive one. Okay? So there is all of our f values from the graph we've been given and now we're going to do the same for G reading off all the values of G from this graph and when X is negative for G is - When it's -3, G is -3. When it's -2, G is -4. When it's negative one G is negative five and it has this horizontal line across to one. So at zero it's still going to be a negative five. And at one it's also going to be a negative five. Now x equals to this function is going up to negative four at x equals three. The function is at negative three At four. The function is at -2 At five. The function is at -1. And finally at six the function is back to negative three. Okay so we have all of our f values, all of our G values that we got. Just by looking at the graphs we were given. And now in order to find F plus G we just add them together F of X plus G of X. So for each point we add together five plus negative two. It's +35 plus negative three is +25 plus negative four is +14 plus negative five is negative +13 plus negative five is negative two three plus negative five is negative 23 plus negative four negative 11 plus negative three is negative two negative one plus negative two is negative 30 plus negative one is negative one and one plus negative three is negative two. And so these are all of the X values and the F plus G values. Okay so now we have X and y values we can go ahead and graph Okay so I'm gonna move down where we have more room to graph and I'm just going to rewrite the X values and the f plus G values we found so that we know what we're graphing and we don't have to keep scrolling up. Okay on your paper you won't have to rewrite them because you should be able to see all of the work you've just done on the same sheet. Okay so again our X. Values in our F plus G values that we just found. We have negative four all the way up positive six for our X. Values. And our F plus G values were + one negative one negative two negative two negative one negative two negative three negative one negative two. Okay so if we grasp this we have our X. Y. Axis and we have positive six. Okay And then 1234 negative four along the X axis. And then our Y axis has a maximum of three and a minimum of negative three. So we have 12 Positive three and two three. Alright so now we're just gonna graph point by point when X is negative four, F plus G. Is three. So we have negative four positive three. One. X. Is negative three. F plus G. S. Two so negative three positive two. X is negative two. F plus G. Is one negative to positive one one, X is negative one, why is negative one and X. Is zero? Y. Is negative two X. Is one, Y is negative two and X is two, Y is negative one And access three, Y is -2. one, X is four, Y is -3. When X is five, Why is -1 and when X is six, Y is negative two. Again we have this line here. This is a straight line, a little bit steeper. Then we get horizontal. Mhm. Like this is our function kind of bounces around a little bit F plus G. Alright, so if we go up and we compare the graph we just drew which is the graph of F plus G. We will see that it looks like the graph and see. So we have the same values as a graph. We just drew and see. Thanks everyone for watching. I hope this video helped see you in the next one.

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

Key Concepts

Function Addition

Graphing Functions

Piecewise Functions

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