Translations Summary

Horizontal Translations

Given an original graph f(x) the transformed graph g(x) = f(x - h), where h represents the horizontal shift.

If h is positive the graph is shifted to the right. If h is negative the graph is shifted to the left.

Because of the equation, the sign of h is the opposite of what it appears.

So in the function (x+2)², h= ^-2 which is a shift left 2

And in the function ln(x-3), h= 3 which is a shift right 3

Vertical Translations

Given an original graph f(x) the transformed graph g(x) = f(x)+k, where k represents the vertical shift.

If k is positive the graph is shifted up. If k is negative the graph is shifted down.

The sign of k matches what it appears.

So in the function x²+2, k = 2 which is a shift up 2

And in the function ln(x)-3, k=^-3 which is a shift down 3

The Key Difference between them is that a horizontal shift happens inside the function and a vertical shift happens outside the function:

inside

g(x) = f(x - h)

(x+2)²

ln(x-3)

outside

g(x) = f(x)+k

x²+2

ln(x)-3

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