What happens if you multiply each x or each y by a positive number?
y=f(ax) is a horizontal stretch or shrink.
y=af(x) is a vertical stretch or shrink.
Practice makes perfect
If our base function is y=f(x), then multiplying either all of the x-values or all of the y-values by a positive number will affect the slope of the function. Let's look at each of the functions given.
y=f(ax)
The graph of y=f(ax) is a horizontal stretch or shrink of y=f(x). We know that it is horizontal because the x-values are changing, they are moving left and right, and the function is either stretching away from or shrinking towards the y-axis. It will be considered a stretch if 01, because each value of x produces a larger value of y. The function is staying farther from the x-axis and is being shrunk with respect to the left and right directions.
y=af(x)
The graph of y=af(x) is a vertical stretch or shrink of y=f(x). We know that it is vertical because the y-values are changing, they are moving up and down, and the function is either stretching away from or shrinking towards the x-axis. It will be considered a stretch if a>1, because each value of y is becoming larger, or "stretched." It will be considered a shrink if 0
