Question

Let f(x)=7^x and g(x)=7^x+2 -4
Which transformations are needed to transform the graph of f(x) to the graph of g(x)?

Select each correct answer.

1. Vertical translation 4 units down
2. Vertical translation 4 units up
3. Vertical translation 2 units up
4. Horizontal translation 4 units left
5. Horizontal translation 2 units right
6. Horizontal translation 2 units left​

Answer 1

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.

Answer 2

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:

$\mathbf{f(x) = 7^x}$

$\mathbf{g(x) = 7^{x + 2} - 4}$

Considering f(x), we have:

$\mathbf{f(x) = 7^x}$

Start by translating the function 2 units left.

The rule of this translation is:

$\mathbf{f'(x) = f(x + 2)}$

So, we have:

$\mathbf{f'(x) = 7^{x + 2}}$

Next, translate the function 4 units down

The rule of this translation is:

$\mathbf{f''(x) = f'(x) - 4}$

So, we have:

$\mathbf{f"(x) = 7^{x + 2} - 4}$

Rewrite as:

$\mathbf{g(x) = 7^{x + 2} - 4}$

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