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 oa. g(x) = fx) - 2 ob. g(x) = fix + 2) oc. g(x) = fx) + 2 od. g(x) = fix-2)

The answer is choice 3.

Step-by-step explanation:

I've had this equation b4

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

Step-by-step explanation:

This is a vertical shift going down. Here is an attachment of my notes on how this transforms a function:

*the note pertaining specifically to this problem starts on the line above the second hole, saying "down three"

The correct option is A.

Step-by-step explanation:

The transformation is defined as

               .... (1)

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

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

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

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.

Therefore the correct option is A.

The correct option is A.

Step-by-step explanation:

The transformation is defined as

               .... (1)

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

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

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

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.

Therefore the correct option is A.

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)

 

 The transformation of f (x) is:

 A. g (x) = f (x) - 4

By looking at the graph, the y component of g is always 2 less than that of f, therefore the best choice is g(x) = f(x) - 2

The first thing we are going to do in this case is to take into account the following definition.
 Translations are transformations that change the position of the graph of a function.
 The general shape of the graph of a function is moved up, down, to the right or to the left.
 The translations are considered rigid transformations. Now we will see how these are performed.
 Vertical translations:
 Suppose that k> 0
 To graph y = f (x) + k, move the graph of k units up.
 To graph y = f (x) -k, move the graph of k units down.
 Using the definition we conclude that:
 g (x) = f (x) - 2
 
 g (x) = f (x) - 2