Question

Use the image to solve the problem below.



What is the k
-value for the horizontal shift from the original function y=f(x)
(solid line) to the translated function y=f(x−k)
(dotted line)?

(1 point)
Responses

3
3

-2
-2

2
2

-3
-3
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Answer 1

To determine the k-value for the horizontal shift from the original function \( y = f(x) \) (solid line) to the translated function \( y = f(x - k) \) (dotted line), we need to analyze the direction and amount of the shift.

- If the dotted line shifted to the right, \( k \) would be positive.
- If the dotted line shifted to the left, \( k \) would be negative.

Assuming that you have visual data to evaluate, here’s how you would identify \( k \):

1. **Locate a key point on the solid line** (for example, where it crosses the y-axis).
2. **Identify the corresponding point on the dotted line.**
3. **Calculate the difference in the x-coordinate values.**

If the dotted line is to the right of the original function by \( k \), then:

- If it is shifted right, \( k \) is positive.
- If it is shifted left, \( k \) is negative.

Based on the options given (3, -2, 2, -3), you can match your calculation to one of these options.

Since I cannot see the image, follow the above steps and select the appropriate value based on the shift you observe. If the dotted line moved right by 2 units, the answer would be \( k = -2 \), and similarly for the other options.