In Exercises 19–24, the graph of an exponential function is given...

Question

In Exercises 19–24, the graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 3^x, g(x) = 3^(x-1), h(x) = 3^x - 1 ; f(x) = -3^x, G(x) = 3^(-x), H(x) = -3^(-x)

Accepted Answer

Hello today we're going to be identifying the function for the given graph. So what we are given is this exponential function that is rotated about the y axis. And it also passes through the point negative one comma six. Now the general form of an exponential function is some base constant raised to the power of X. But as you can see here this graph has been rotated about the Y axis. So in order for us to rotate an exponential function about the Y axis, the X is going to need to have a negative sign in front of it. So the general form of this graph is going to be B to the power of negative X. Now we need to identify what the base is going to be. What this is saying is if we plug in the value of negative one into our function, this is going to give us the value of six. So what we're doing here is plugging in negative one for B. And B to the power of negative negative one is just going to give us B. So we have the base is equal to six. And if we replace B in our general function we get F. Of X is equal to six to the power of negative X. And this is going to be the function for the given graph. And with that being said, the answer to this problem is going to be a So I hope this video helps you in understanding how to approach this problem and I'll go ahead and see you all in the next video

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In Exercises 19–24, the graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 3^x, g(x) = 3^(x-1), h(x) = 3^x - 1 ; f(x) = -3^x, G(x) = 3^(-x), H(x) = -3^(-x)