Graph f(x) = 2^x and its inverse function in the same rectangular...

Question

Graph f(x) = 2^x and its inverse function in the same rectangular coordinate system.

Accepted Answer

Hey everyone in this problem we are given the function G of X is equal to three to the exponent X. And we're asked to draw the graph of the function and its inverse in the same Cartesian plane. Alright, so we're given a function, we are asked to draw a graph. Let's go ahead and use a table of values. Okay, now when we're looking at possible X values, okay. We see that our um answer choices go from about negative five to kind of positive five range. When we're looking at G it kind of goes off after about X equals positive three. Okay. Kind of levels out in those negative. So let's start with the table of values that goes from negative to positive three and see if that gets us enough information to do our graph. So we have X. And we have a function G of X Which is equal to 3 to the exponent X. We're gonna start at - -1012. Yeah. Alright, so when X is -2, RGFX is going to be 3 to the exponent -2. This is going to be equal to 1/3 squared Equal to one overnight. Alright, when X is negative one we get three to the negative one. Okay, this is equal to 1/3. When X is zero with three to the exponent zero which gives us just one, one, X is one. We have three to the exponents one which is three one X is two, we have three to the exponent to which gives us nine and one X is 33 to the exponent three gives us 27. Alright, so we have this table of values. So let's start making our sketch. So All right. We're gonna try to match the axis of the ones given. Okay, so they're gonna go up to positive 14 4, 6, 8, 10, 12. So it's close to 468, And then 2 123. So this is 24 and same in the negative. Alright, so let's graph the function G. Of X in red. So G of X is going to be in red And we have the points so at negative to our functions at one overnight. So it's kind of just above zero negative one, it's one third. So again just above zero At zero or function is at one. So we have this point here, 01 At one. Function is at three. That to our function jumps to nine and then a three year function is way up out of. So we connect these dots, we kind of get a function that looks like, oops, let's just try to straighten that out at the end. This is what our function is gonna look like G of X. And we see that we've written this 0.1 here. Okay, where we cross that Y axis. Again these are standard access X and Y. If we look at our answer choices. Okay, we're comparing the red curve we've drawn in red as well. We see that the only one that crosses the Y axis and has the 10.1 is option a option B has a 0.2 which we know is not in G of X. C has a 0.0 which we know is not G. Of X and D has a 0.9 which we know is not in G. Of X. Okay, so even without looking at the inverse, we can already narrowed down to option A. Alright, well, let's look at the universe. Hate to see how it would go about this. Well, when we have an inverse. Okay, so if we have X M G inverse of X. Now we know the function G is three of us. So you can go ahead and find what the inverse is. But when you have a table of values, what you can also do is just swap the values. So When X is one, why is going to be zero? Starting with this 01, pair, one, X is three. Why is going to be one When X is nine, Why is going to be too? I want x is 27. Why? It's going to be three. Okay, so we've used the property or or inverse where we swap the X and Y values. So we've made our table values. We don't need to go ahead and find the inverse function on the breakaway. We can just swap those values to give us some points that we can graph. So now we can graph these phones. We have 10. We have three and 1. We have nine, which is way down here. Okay. And two. So you can see that our function does something like this. So if we go back up to the top and let me actually label this guy first. This is the graph of G inverse. The green graph just like the green ones shown above. So if we go back up to the top, we see that this matches from a as well. Okay, we have this .10 that we've drawn and then it kind of continues up like this. And so the graph of the function, the graph of the inverse. Those match the graphs shown an egg kgs of function three to the exponent X. And and we have G inverse. Thanks everyone for watching. I hope this video helped see you in the next one.

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Graph f(x) = 2^x and its inverse function in the same rectangular coordinate system.