transformation of functions

Question

find g(x) where g(x) is the translation 4 units right and 2 units down of f(x)= - (x-3)^2+8

Answer 1

Moving left or right goes "with" the x but opposite. Moving up or down goes "outside" the x.

g(x) = -(x - 3 - 4)² + 8 - 2

g(x) = -(x - 7)² + 6

Answer 2

g(x)= -(x-3-4)²+8-2

Simplify by combining like terms

g(x)= -(x-7)²+6

Answer 3

You need to learn how to move left, right, up, down, and shrink/expand vertically and horizontally. The pdf referred to here goes over all of this.

https://www.shsu.edu/~kws006/Precalculus/1.3_Function_Transformations_files/1.3%20Function%20Transformations%20slides%204to1.pdf

Also, some Khan Academy you tubes cover the topic

This example uses two of these transformation. We move to the right an amount a by subtracting a from x (we subtract because that means x has to increase an amount a so that (x-a) + a = x) We move down by b by subtracting b from the function.

Thus, for f(x)= - (x-3)^2+8, we move right 4 and down 2 by subtracting 4 from x and down 2 by subtracting 2 from the function.

Thus, g(x) = - ((x-4)-3)^2+8 - 2 = -(x-7)^2 + 6