2 The graph of y fx is given below Use it and Theorem 17 to

2

The graph of y = f(x) is given below. Use it and Theorem 1.7 to graph the given transformed function. y = 4-f(4-x) y = f(x + 3)

Solution

We know that:

i. The grapf of f (-x) is the graph of f(x) reflected in the y-axis

ii. The grapf of - f (x) is the graph of f(x) reflected in the x-axis

iii. The grapf of f (x + c) is the graph of f(x) shifted to the left c units

iv.The grapf of f (x - c) is the graph of f(x) shifted to the right c units.

v.The grapf of f (x)+ c is the graph of f(x) shifted upwards c units

vi. The grapf of f (x) - c  is the graph of f(x) shifted downwards c units

a) y = 4 - f(4 -x) We will consider the changes in stages:

1. The graph of f (-x) is the graph of f(x) reflected in the y-axis

2. The graph of f(4 -x) is the graph of f(x) reflected in the y-axis and then shifted to the left 4 units

3. The graph of - f (4- x) is the graph of f(x) reflected in the y-axis and then shifted to the left 4 units and then  reflected in the x-axis

4.  The graph of 4 - f (4- x) is the graph of f(x) reflected in the y-axis and then shifted to the left 4 units and then  reflected in the x-axis and then shifted upwards 4 units

b) y = f (x + 3) is the graph of y = f(x) is the graph of f(x) shifted to the left 3 units