Respuesta :
Answer:
1.- Vertical translation 4 units down
6.- Horizontal translation 2 units to the left
Step-by-step explanation:
Notice that the addition of 2 units to the variable "x" in the exponent involves a horizontal shift to the left in 2 units.
Notice as well that a subtraction of 4 units to the functional expression involves a vertical shift downwards in 4 units.
Transformation involves changing the form of a function
The transformations are:
- vertical translation 4 units down.
- horizontal translation 2 units left.
The functions are given as:
[tex]\mathbf{f(x) = 7^x}[/tex]
[tex]\mathbf{g(x) = 7^{x + 2} - 4}[/tex]
Considering f(x), we have:
[tex]\mathbf{f(x) = 7^x}[/tex]
Start by translating the function 2 units left.
The rule of this translation is:
[tex]\mathbf{f'(x) = f(x + 2)}[/tex]
So, we have:
[tex]\mathbf{f'(x) = 7^{x + 2}}[/tex]
Next, translate the function 4 units down
The rule of this translation is:
[tex]\mathbf{f''(x) = f'(x) - 4}[/tex]
So, we have:
[tex]\mathbf{f"(x) = 7^{x + 2} - 4}[/tex]
Rewrite as:
[tex]\mathbf{g(x) = 7^{x + 2} - 4}[/tex]
Hence, the transformations are: vertical translation 4 units down and horizontal translation 2 units left
Read more about transformations at:
https://brainly.com/question/13801312