Question

Let f(x) = 4^x and g(x) = 4^(2x+1) - 3. Which transformations are needed to transform the graph of f(x) to the graph of g(x? Select EACH correct answer.

Option 1: Vertical translation 3 units down.
Option 2: Horizontal translation 1 unit left.
Option 3: Horizontal translation 3 units right.
Option 4: Vertical translation 1 unit down.
Option 5: Horizontal translation 1 unit right.
Option 6: Vertical translation 3 units up.

Answer 1

To transform the graph of f(x) = 4^x to the graph of g(x) = 4^(2x+1) - 3, vertical translation 3 units down and horizontal translation 1 unit left are required transformations.

Step-by-step explanation:

To transform the graph of f(x) = 4^x to the graph of g(x) = 4^(2x+1) - 3, we need the following transformations:

1. Vertical translation 3 units down: This means we need to shift the graph downward by 3 units.
2. Horizontal translation 1 unit left: This means we need to shift the graph to the left by 1 unit.

Therefore, Option 1 (Vertical translation 3 units down) and Option 2 (Horizontal translation 1 unit left) are the correct transformations needed.