Example 14 Two graphs are shown below. Relate the function g(x) to f(x). f(x) 5+ 4+ 3+ 2+ 1+ Show solution 0 g(x) 54 4- 3- 2- X A Notice that the coefficient needed for a horizontal stretch or compression is the reciprocal of the stretch or compression. To stretch the graph horizontally by 4, we need a coefficient of 1/4 in our function: f I This makes the inputs come in 1/4 as fast, so the function takes 4 times longer to increase and decrease. = It is useful to note that for most toolkit functions, a horizontal stretch or vertical stretch can be represented in other ways. For example, a horizontal compression of the function f(x) result in a new function g(x) = (2x)2, but this can also be written as g(x) = 4x, a vertical stretch of x by would f(x) by 4. When writing a formula for a transformed toolkit, we only need to find one transformation that would produce the graph. Exercise 1.5.7 Write a formula for the toolkit square root function f(x)= horizontally stretched by three T