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 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. 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.