Graph each function. See Example 2. ƒ(x) = (1/10)^-x

Question

Accepted Answer

Hello everybody. A all right. Today they are going to be looking at this math question that states plot the given function on the rectangular coordinate system where our function is AX is equal to the fraction one divided by 30 and that fraction to the exponent negative X. Now, when looking at a question like this, I'm gonna ask myself, what is the parent function here? So the general function or the parent function here would be F of X is equal to A, to the negative X where A is any constant. In this case R A is equal to one divided by 30. So our parent function here is a to the exponent negative X. So let's ask ourselves what different rules we have for this graph. So I'll do a simple recall of what happens when we have a graph of A to the exponent negative X. So the first thing I'll know is I'll make point number one which is with a graph of A to the exponent negative X. We have a point at negative one comma a, a point at zero comma one and a point at one comma one divided by A Now again, in our case, A is equal to one divided by 30. So we'll have the points negative one comma one divided by 30. We'll have the same 0.0 comma one. And finally, we'll have the 0.1 comma 30 because it should be one comma one divided by A and one divided by one divided by 30 is just 30. So those are gonna going to be three points in our graph, then I can make another point, point B or 0.0.2. This will be our second point. So we'll have that if A is greater than one F of X is decreasing and we'll also have that if zero is less than A is less than one. So if A is between zero and one F of X is increasing and now, like we said before, A equals one divided by 30 and zero is less than one divided by 30 which is less than one. Therefore, our F of X is increasing. And finally, I'll make point number three, which is for a graph of A to the exponent negative X, the X axis is an Asymptote. So those are three rules for a graph of A to the exponent negative X where R A is one divided by 30. So now with this information, we can go ahead and graphic graphic are function. So let's do that. So we'll have a Y axis and an X axis and we'll have a point at zero comma one, we have a point at one comma and we'll have a point at negative one comma one divided by 30. Now, we can connect those points and keep in mind that as we said, our function is increasing for after um our Y A R Y intercept, so we'll be increasing from zero comma 1 to 1 comma 30. And before that, we will be decreasing, almost touching the X axis but never touching our horizontal aci tode. So I hope that was helpful. And until next time.

Graph each function. See Example 2. ƒ(x) = (1/10)^-x

Key Concepts

Exponential Functions

Graphing Techniques

Transformations of Functions

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