Q. Scaling and translation for equations?

Ans.

If you have an equation in the form y= f(x) (if you're not familiar with functions, that just means having "y" on the left side and some expression involving x on the right), you usually do vertical translation and scaling differently than is shown in the other sections of this chapter. For example, take the equation

y = x² + x.

If you want to shift the graph vertically, you would typically add or subtract from the variable y. To shift upward by 1, for instance, you would write

y - 1 = x² + x.

However , since the original equation was in the form ofy = f(x), we might want to tkeep it that way. In this case, we just moved the 1 over to the right:

y = x² + x + 1.

Thus, a positive 1, added to the right side of the equation, causes an upward shift. Similarly, if we want to stretch the graph vertically by a factor of 2, the normal technique is to write

y= x² + x,

2

but if we want to keep the equation solved for y, we would write instead

y= 2(x² + x).

You've probably already seen these tricks, applied to trigonometric functions.