Write an equation for the following transformation of y = x a vertical stretch by a factor of 6.
y = 6x, y = x/6, y = x + 6, y = x - 6

Solution:

In vertical stretch transformation the following needs to be noted:

1. When either f(x) or x is multiplied by a number, functions can “stretch” or “shrink” vertically or horizontally, respectively when graphed.
2. In general a vertical shrink is given by the equation y = bf(x) = f(bx) where b > 1
3. In general a horizontal stretch is given by the equation y = cf(x) = f(cx) where 0 < c <1

The above can be demonstrated with help of a diagram where three curves are plotted:

1. y = x (original function)
2. y = 6x (function vertically stretched)
3. y = x/6 (function horizontally stretched)

When x is multiplied by 6 the function y stretches vertically i.e. becomes closer to y axis.When x is divided by the function y spreads horizontally (moves away from the y axis).

Hence y = 6x vertically stretches the function.

Write an equation for the following transformation of y = x a vertical stretch by a factor of 6.

Summary:

The equation for the following transformation of y = x a vertical stretch by a factor of 6 is given by y = 6x.