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 figuring out the function for the given graph. So what we are given is this exponential function? Who's horizontal ascent tote is that Y is equal to zero and passes through the 00.1 comma six. So the general form of an exponential function is F. Of X. Is equal to some constant base be raised to the power of X. And looking at the given graph, there seems to be no transformations applied to the original function. So we're going to need to figure out what the base B is for a general function. Let's take a look at the 0.1 comma six. What this is saying is that if I plug in the value of one to our function this is going to spit out the value of six. So if I plug in the value of one to our general function we're going to get F of one is equal to B to the power of one which is equal to six. And we can go ahead and use this statement to solve our base B, B to the power of one is just going to give me B. So what I am left with is B is equal to six. And if I take this value and replace it for be in our general function, what I get is the function F. Of X is equal to six to the power of 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 be. 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)