describe the transformation of the following functions

Question

1. g(x-3)

2. g(x)-4

3. g(x+3)

4 g(x)+1

Answer 1

Hi, Shaun.

To answer these questions, you need to know the effect of adding or subtracting a constant either inside or outside a function. When a constant is added/subtracted outside a function, a vertical translation occurs. When a constant is added/subtracted inside a function, a horizontal translation occurs. Here are the general rules:

The graph of g(x - h) is the graph of g(x) translated h units to the right when h > 0 and translated |h| units to the left when h < 0.

The graph of g(x) + k is the graph of g(x) translated k units up when k > 0 and translated |k| units down when k < 0.

So, the answers to the four problems are:

1. The graph of g(x - 3) is the graph of g(x) translated 3 units to the right.
2. You can write g(x) - 4 as g(x) + (-4). So, the graph of g(x) - 4 is the graph of g(x) translated |-4| = 4 units down.
3. You can write g(x + 3) as g(x - (-3)). So, the graph of g(x + 3) is the graph of g(x) translated |-3\ = 3 units to the left.
4. The graph of g(x) + 1 is the graph of g(x) translated 1 unit up.

Doug