Use the images to answer the question. Original function: Translated function: Notice the horizontal shift in the images. What is the value of k for the horizontal shift that occurred between the graph of the original function y=f(x) and the graph of the translated function y=f(x−k) ? (1 point)

Answer 1

To determine the value of \( k \) for the horizontal shift between the original function \( y = f(x) \) and the translated function \( y = f(x - k) \), we need to identify the direction of the shift.

1. If the graph of the translated function \( y = f(x - k) \) is shifted to the right compared to the original function \( y = f(x) \), then \( k \) is positive.

2. If the graph is shifted to the left, then \( k \) is negative.

In general, the relationship can be described as:

• A horizontal shift to the right by \( k \) units corresponds to \( k > 0 \).
• A horizontal shift to the left by \( k \) units corresponds to \( k < 0 \).

To find the exact value of \( k \), you would compare the position of a known point on the original function to the corresponding point on the translated function and calculate the difference.

In short, you assess the direction and distance of the shift to conclude on the value of \( k\). If you provide how far the function was shifted or any associated numerical values, I could assist further in determining \( k \).