Question

PLEASE HELP!!!! If a function, f(x) is shifted to the left four units, what will the transformed function look like?

Answer 1

If you shift f(x) to the left four units, then the coordinate axis effectively moves four units to the right. This "four units to the right" movement for the axis means that every x is replaced with x+4.

So that means f(x) turns into f(x+4)

For example, say we had the function f(x) = 5x^2 + 10x
Shifting f(x) four units to the left leads to
f(x) = 5x^2 + 10x
f(x+4) = 5(x+4)^2 + 10(x+4) ... notice the replacements in bold
f(x+4) = 5(x^2+8x+16) + 10(x+4)
f(x+4) = 5x^2 + 40x + 80 + 10x + 40
f(x+4) = 5x^2 + 50x + 120