In Exercises 32–35, the graph of a logarithmic function is given....

Question

In Exercises 32–35, the graph of a logarithmic function is given. Select the function for each graph from the following options: f(x) = logx, g(x) = log(-x), h(x) = log(2-x), r(x)= 1+log(2-x)

Accepted Answer

Hello everyone in this video, we're going to be looking at this logarithmic graph and we want to try and figure out the equation of this logarithms based off of this graph. So just off of seeing it it seems like it follows the normal logarithmic equation where it has the form F. Of X is equal to log of X. However, that is not one of the answer choices. So let's see which of these answer choices make sense. So for this first answer choice, we have an X -1. And when we have an x minus a number inside of that log the graph gets shifted C units to the right. So in this case C is equal to one. So the graph could be shifted to the right by one unit and that makes sense. This point could be 20 instead of the usual 10. So we're going to say it could be an option B is stating one plus or x plus one and when you have a plus instead of a minus now you've shifted the graph c units to the left. Which means that the graph would have an X intercept of zero or it would pass through the origin because this original logarithm logarithmic occasion with no shift has an x intercept of 10. If we shifted over One to the right we're going to have the next intercept of 20. But if we shifted over to the left, one unit since he is equal to one, we would have The next intercept of 00. And we're not seeing that in this graph, there is no line going through 00. So seems like option B is not The one for us. And now we have C. Which I'm going to rearrange so C. Of X. Is equal to log negative X plus one. So here you can see that we have this plus one again which means that I already don't like this answer. And then there's also a negative which means that the graph would be going the opposite way. It would be on the sort of other side of the y axis. And that's because of the negative here on the X. R. Original graph gets reflected across the Y axis. So I know that C. Is not a good option for me. And if we look at D you can see that there's a vertical translation and once again that reflection. So based off of just the reflection, I can say that D. Is not for me but also we have no vertical translation here because the X intercept seems to still pass through normal points. Um However, even if there was a vertical translation, this equation gets eliminated because we're not reflecting it across the y axis. So it looks like choice A. Is the best option. So I'm gonna say is our final answer. So hopefully this video helped and see you next time

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In Exercises 32–35, the graph of a logarithmic function is given. Select the function for each graph from the following options: f(x) = logx, g(x) = log(-x), h(x) = log(2-x), r(x)= 1+log(2-x)