36.7k views
1 vote
Suppose the function f(x) is transformed and the new rule for the translated function, g(x), is g(x) = f(x + 6) - 4. Describe this transformation.

1 Answer

4 votes

Final answer:

The function g(x) = f(x + 6) - 4 represents a horizontal shift of 6 units to the left and a vertical shift of 4 units downward of the original function f(x).

Step-by-step explanation:

When the function f(x) is transformed into the function g(x), the rule g(x) = f(x + 6) - 4 represents two specific transformations. The part where we see x + 6 inside the function indicates a horizontal shift of the graph of f(x) by 6 units to the left. This is because adding a positive number inside the function's argument moves the graph in the negative x-direction. Conversely, subtracting within the argument moves the graph in the positive x-direction.

Additionally, the "- 4" at the end of the function g(x) signifies a vertical shift. The graph of f(x) is moved downward by 4 units. When a constant is added or subtracted to the function outside of its argument, it results in a vertical translation. Specifically, subtracting 4 moves the graph downwards, while adding would move it upwards.

To summarize, the function g(x) = f(x + 6) - 4 is the result of taking the graph of f(x) and shifting it 6 units to the left and 4 units down. These transformations do not affect the shape of the graph; they merely reposition it within the coordinate plane.

User Suselrd
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.