vertical stretch vs vertical compression

Vertical stretch vs vertical compression free#

Take note of the new critical points, such as the new maximum point of the graph.This means that when applying vertical stretches on a base graph, its x-intercepts will remain the same.Ensure that the values for x remain the same, so the base of the curve will not change.Here are some things to remember when we vertically stretch functions: When given a function’s graph, we can vertically stretch it by pulling the curve outwards based on the given scale factor. Hence, the resulting function is 5(5x + 1) = 25x + 5. This means that if f(x) = 5x + 1 is vertically stretched by a factor of 5, the new function will be equivalent to 5 The input values will remain the same, so the graph’s coordinate points will now be (x, ay). f(x) will stretch the base function by a scale factor of a.How do we generalize this rule? When we have |a| > 1, a We can also see that their input values (x for this case) remain the same only the values for y were affected when we stretched f(x) vertically. When f(x) is multiplied by scale factors of 3 and 6, its graph stretches by the same scale factors. Why don’t we observe how f(x) is transformed when we multiply the output values by a factor of 3 and 6? The graph below shows the graph of f(x) and its transformations. When a function is vertically stretched, we expect its graph’s y values to be farther from the x-axis. This results in the graph being pulled outward but retaining the input values (or x). Vertical stretch occurs when a base graph is multiplied by a certain factor that is greater than 1. We’ll now discuss the third transformation technique: vertical stretching.

Vertical stretch vs vertical compression free#

Refresh your knowledge of vertical and horizontal transformations.įeel free to click on the links to refresh your knowledge on these essential topics.Understanding the common parent functions we might encounter.When a base function is multiplied by a certain factor, we can immediately graph the new function by applying the vertical stretch.īefore we dive deeper into this transformation technique, it’s best to review your knowledge on the following topics: Vertical stretch on a graph will pull the original graph outward by a given scale factor. Hopefully that helps.Vertical Stretch – Properties, Graph, & ExamplesĮver noticed graphs that look alike, but one is more vertically stretched than the other? This is all thanks to the transformation technique we call vertical stretch. And you'll see over and over again that to get the same value, you have to put two times as much into f as you have to put into g. Find the corresponding points where the f's and the And if that doesn't make intuitive sense, you can also just try Is going to increase or become negative faster so it thins it up. Input into a function by a number larger than one, it's going to compress. One way to think about it when you take, when you multiply the It looks optically like that and we shrunk it down. Out of the function when you input two times that into f of x. Whatever the x that you input into g of x, you get that same value 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