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Refer to the functions f and g given by the graphs below (the domain of each function is $[-2,2]) .$ Use the graph of for $g$ as required, to graph each given funct...

Question

Refer to the functions f and g given by the graphs below (the domain of each function is $[-2,2]) .$ Use the graph of for $g$ as required, to graph each given function.(GRAPH CANNOT COPY)$$g(x-1)$$

Refer to the functions f and g given by the graphs below (the domain of each function is $[-2,2]) .$ Use the graph of for $g$ as required, to graph each given function. (GRAPH CANNOT COPY) $$g(x-1)$$



Answers

Refer to the functions f and g given by the graphs below (the domain of each function is $[-2,2]) .$ Use the graph of for $g$ as required, to graph each given function. (GRAPH CANNOT COPY) $$g(x-1)$$

Okay, so we want to roll rate the following using our graph in her book. So let's rewrite this as G, composed of G evaluated at negative two. So we need to first find G evaluated at negative two. So when X is equal to negative two or G value is equal to a positive one. So we can write this G evaluated at one and when acceptable to one RG value that's equal to four. So we see that this year is equal to four.

Okay, So we have Why equals f of X graft? This represents open circles. This represents close circles when we doing whoever he used blue for this in green for this. So we have a lot going on in this one. We have a vertical shrinkage, a reflection over the X axis, and we're gonna move it to the left to Tom's. They're two units. So let's go ahead and move it to the left. Now, that's gonna be negative. 60 negative to negative two negative to zero. And too negative too. Now I'm going to reflect that across the Y axis. So we need to multiply our why coordinate but negative ones. That gives us negative 60 Take it to two, negative to zero. And then to to know for the shrinkage, we need to multiply the y coordinate by 1/2. So that is going to be negative. 60 to native to one, negative to zero and then to one. Because if you multiply to but when half something is dividing by two. So you get this. Now I'm gonna do these in blue and these in green. So let's start with their blue. We have negative. 60 native to zero. We've got negative 21 and then we've got to one. So it looks like it was originally 12 but it looks like we're just gonna blend it up straight through here. And our midpoint is 1/2. So blue represents our new equation. Blacker prisons are

For this problem. We want to match the equations on the left, to the grafts on the right. And when we look at the graphs of F and G, we're going to generalize because we just are focusing on the shape and the direction of each graph. We're going to generalize that after Becks is linear, so it's gonna equal X. And since G of X is a problem facing upwards, we're going to generalize it. T equal x squared a quadratic. So for our 1st 1 f plus g of X. If we plug in f of x and g of X week, it x plus X squared. So we will need to find a graph that has a problem facing upwards. And the only graph that has that is graft for so that is our answer for F plus g vexed men Prep minus G of X. We get a minus X squared. So since we have a negative in front of our quadratic value, we want to look for a graph that has a problem facing downwards. And the only one that has a problem facing downwards is number one. That's our interpreter at minus G. M. X then for F times G of X, we would have X times X squared, which is X cubed. So we're looking for a cubic function and the only cubic function that we have as a graph is number two and finally for F divided by G of X. We have X over X squared, which is one over X. So if we're looking for a graft, represent that we have graft number three.

Just so we're given that each of excessive good to have composed of G services equals F of G of X. So let's see. So why don't we set g of X TV equal to X and an half of axe to be equal to three, So we would have composed of G of X? So what's your backs? That would give us a 303 that would give us a thanks, and enough of X is equal to three.


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