![]() When combining transformations, it is very important to consider the order of the transformations. This means that the input values must be four times larger to produce the same result, requiring the input to be larger, causing the horizontal stretching. Our new population, R, will progress in 1 hour the same amount as the original population P does in 2 hours, and in 2 hours, the new population R will progress as much as the original population P does in 4 hours. Let’s let our original population be P and our new population be R. ![]() Suppose a scientist is comparing a population of fruit flies to a population that progresses through its lifespan twice as fast as the original population. If the constant is between 0 and 1, we get a horizontal stretch if the constant is greater than 1, we get a horizontal compression of the function. When we multiply a function’s input by a positive constant, we get a function whose graph is stretched horizontally away from or compressed horizontally toward the vertical axis in relation to the graph of the original function. ![]() Notice that we are changing the inside of a function. Now we consider the changes that occur to a function if we multiply the input of an original function f\left(x\right) by some constant.
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