Question

Two exponential functions, f and g, are shown in the figure below, where g is a transformation of f.

Which of the rules given below shows the transformation of f?

A. g(x) = f(x) - 4

B. g(x) = f(x - 4)

C. g(x) = f(x) + 4

D. g(x) = f(x + 4)

Answer 1

The correct option is A.

Explanation:

The transformation is defined as

`g(x)=f(x+a)+b` .... (1)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

From the given graph it is clear that the function f(x) shifts 4 units down to get g(x). So, the value of b is -4 and value of a is 0.

`g(x)=f(x+0)+(-4)`

`g(x)=f(x)-4`

Therefore the correct option is A.

Answer 2

The first thing that we must observe for this case is the intersection of the functions with the y axis.

We observed that:

f (0) = 2

For the function g (x) we have:

g (0) = -2

Therefore, we can rewrite g (x) as:

g (x) = f (x) - 4

Looking for intersection with axis and we have:

g (0) = f (0) - 4

g (0) = 2 - 4

g (0) = -2 (correct demonstration)

Answer:

The transformation of f (x) is:

A. g (x) = f (x) - 4