Question

Consider the functions f(x) and g(x). The function f(x)=2x-5 and g(x)= -f(x+1)+3. A. Describe the three transformations that are performed on f(x) to create g(x).1.2.3.B. Sketch a graph of g(x):

Answer 1

First we have to take a look at the expression f(x + 1). This represents an horizontal translation. So this is the first transformation:

1. Horizontal translation

Now we can see that we have to multiply f(x + 1) by -1. This represents a reflexion on the y-axis

2. Reflection on y-axis

Finally we can see that -f(x + 1) is added by 3 units. This represents a vertical translation:

3. Vertical translation

Answer:

1. Horizontal translation

2. Reflection on y-axis

3. Vertical translation

Now let's see the final function:

f(x) = 2x - 5

f(x+1) = 2(x + 1) - 5

f(x+1) = 2x + 2 - 5

f(x+1) = 2x - 3

g(x) = -2x + 3 + 3

g(x) = -2x + 6

So let's plot f and g on the same reference system: