![]() Well, whatever we have here, it's f of twice that. Or if you wanted to think of it the other way, if you want to think of the other way, if you want to say g of x is going to be f of. Is going to be equal to g of, well whatever you have it here, it seems like we have And so in general, it looks like for given x. Same part of the function if we assumed g of x is a Optically I'm just looking at, well, looks like it's the And once again, I'm lookingĪt the where the functions hit the same value and also F of two looks like itĬorresponds to g of one. If you look at f is, so f of two, looks like it corresponds to g of one, f of two corresponds to g of one. Three, g of negative three right over there. If you apply the transformationĪt the point f equals, at the point negative sixĬomma f of negative six. Let's see, it looks like f of negative six and it is equal to g of negative three. Point right over there is g of negative three. So we wanna find the corresponding points. Or it gives us the same value as f of negative six. More meat on that bone and see if we can identifyĬorresponding points. That's what g of x looks like but let's put a little bit It seems like if you were to compress it to towards the center, Immediately look like it, it looks like g of x is kind ofĪ thinned-up version of f of x. Video and see if you can give a go at it and then G of x in terms of f of x?" And like always, pause the Is y is equal to f of x, the solid blue line, This is y is equal to g We can combine this stretching and compression in four different ways in any log function.Transformation of f of x. The a and b refer to the a and b values in our general logarithmic function. We can summarize our stretching and compression information in this table. The function (1/2)log(3 x) for example has both a vertical compression and a horizontal compression. We can have log functions that use a combination of the above. Our red is log( x), our blue is (1/2)log( x), our green is (1/3)log( x), and our purple is (1/4)log( x).Īs our a values get smaller than 1 but still stay above 0, our log function gets smaller vertically. If you guessed that we get vertical compression when our a values are between 0 and 1, then you guessed right. We can see that we have vertical stretching as our function goes higher and higher as we increase our a values to greater than 1. What do you notice about these graphs that is different than the graphs for horizontal stretching and compressing? Do you see how the x-intercept remains the same for all the log functions? When we don’t change the b value of our log function, then our x-intercept won’t change. Here we have log( x) as red, 2log( x) as blue, 3log( x) as green, and 4log( x) as purple. ![]() Let’s see what the graph does for log( x), log( x/2), log( x/3), and log( x/4). If our b value is less than 1 but greater than 0, then we will have horizontal stretching. The more we compress, the smaller our x-intercept is. Now, look at where these functions cross the x-axis.ĭo you see that it is moving? As our b values become greater than 1, our x-intercepts decrease. The red graph is the log( x) function, the blue graph the log(2 x) function, the green graph the log(3 x) function, and the purple graph the log(4 x) function. For the log function where our a and b is 1, f(x) = log( x), we get a graph like this. This is the log function that is used in calculators. We can have a log function to the second, third, or fourth base and so on. Remember, our log function can have different bases. Our general logarithmic function is of this form: So, vertical compression means we make the function smaller vertically. ![]() When we compress a function, we make it smaller in a way. So, horizontal stretching means we make the function bigger horizontally. When we stretch a function, we make it bigger in a way. The kinds of changes that we will be making to our logarithmic functions are horizontal and vertical stretching and compression. You will know when you are looking at a logarithmic function because you will see the log operator. * All Partners were chosen among 50+ writing services by our Customer Satisfaction Team ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |