Graph each function.

Question

ƒ (x) = (1 / 6)^{- x}

Accepted Answer

Welcome back everyone. In this problem, we want to draw the graph of the function F of X equals an eighth to the power of negative X. For our answer choices, we have possible solutions of what this graph will look like. This is what it will look like. For me, this is what it will look like for AC and here's a possible solution for D. And now when you look at the answers, you'll notice that they all have a few points that are already plot and identified on our graph. So this tells us that if we figure out what points are supposed to be on our graph, then we can get an idea of what our graph will look like. So let's first start by trying to plot a few points on our graph for our function. OK. So we can start by trying to find the Y intercept. OK. And now to do that, we know the Y intercept is at X equals zero. So we can do it by finding F of zero. Now F of zero is going to be equal to an eighth raised to the power of negative zero, which is an eighth to the power of zero, which simply equals one. So that tells us then that 01 is the Y intercept of our graph. Next, we can try to find a few more ordered pairs and we can do that by quickly setting up a table of X and F of X values. OK. And let's say that we wanted to find it from negative to all the way up to positive three. Now, in the same way that we found our Y intercept, we can find our F of X values for our varying values of X. For example, when X equals negative two, then F of negative two is going to be equal to an F raised to the power of negative negative two. When X equals negative one, then F of negative one equals an F raised to the power of negative negative one and so on. OK? Now you can go ahead and work this out. But when you do, you should find that when X equals negative two F of X equals 164 when X equals negative one, F FX is an eighth, we already know that when X is zero, F FX is one, when X is one, F FX is eight, when X is two, F FX is 64. OK? And when X is three, F FX is 512. OK? No, we know as well that because our power is negative, OK? Our power is negative X, we can tell that based on our function, the horizontal Asymptote for it is the X axis. In other words, for this case, as X increases, OK, then it's going to get closer f of X is going to get closer and closer to the X axis but never touch the X axis. OK. So now to figure out which one is correct, we need to find our graph that is going to have the ordered pairs as stated in our table, we could do a quick sketch here. Now, what we're essentially saying is that we want to find a graph such that if we label this negative two, negative 1012 and three, OK. When X is negative two, F FX is 1 64th when it's negative one, F FX is an eighth when it's zero. OK? It equals one. OK. Zero equals one when it's one F FX is eight when it's two, F FX is 64. So that's probably gonna be off a graph and when X is three, it's 512. OK. So in other words, we want to find our graph because our graph will probably look something like this. You know what as well. Let me just fix this value for 1 64th because it's actually smaller than an eighth. So it would probably be somewhere down here. So our graph is going to probably look something like that. So now let's look at our answer choices, which one of these has those points. Well, by looking, we can tell it's not A, OK. A is set in the opposite direction. OK? If we look at B, we notice here that B is also set in the opposite direction, plus it says that when X is one, F FX is +98, which we know is not true. When we look at answer choice C we can see that it is 1801 negative one and 1/8 and it's in the shape of the graph we sketched. So C is the right answer and we can be sure we're right because when we look at D, our graph is set the other way. So we know that it's incorrect. Therefore, C is the correct graph of negative A raised to the sorry, the correct graph of an eighth raised to the power of negative X. Thanks a lot for watching everyone. I hope this video helped.

Graph each function. $ƒ (x) = (1 / 6)^{- x}$

Key Concepts

Exponential Functions

Graphing Techniques

Transformations of Functions

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