Describe the transformation that occurs in the graph when changing an equation from f of x equals negative X to f of x equals negative x + 4

Question

The original function ships horizontally to the right four units the original function shifts horizontally to have four units the original functions vertically up for units original function ships vertically down for units

Answer 1

To understand the transformation from the function \( f(x) = -x \) to \( f(x) = -x + 4 \), we can break it down step by step.

1. Original Function: The graph of \( f(x) = -x \) is a straight line with a slope of -1 that passes through the origin (0, 0).

2. Transformed Function: The transformed function \( f(x) = -x + 4 \) can be analyzed through its components.

   • The term \(-x\) retains the same slope of -1 and the same orientation as the original function, meaning it still has the same line but simply translated.
   • The \(+ 4\) indicates a vertical shift of the entire graph.

Transformation Description:

• Vertical Shift: The addition of 4 in the function \( -x + 4 \) shifts the graph vertically upward by 4 units. This means that every point on the line \( f(x) = -x \) will be moved up by 4 units.

Thus, the correct transformation from \( f(x) = -x \) to \( f(x) = -x + 4 \) is that the original function shifts vertically up 4 units.

Therefore, the answer is: the original function shifts vertically up 4 units.