Use the image to answer the question.

Question

Two S-shaped curves are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1.

The graph shows a parent function y=f(x)
(solid line) and its translated form y=f(x)+k
(dotted line) which has undergone a vertical shift. Use the graph to find the value of k.

(1 point)
k=

Answer 1

To determine the value of \( k \), we need to assess the vertical shift of the dotted line (the translated function) compared to the solid line (the parent function).

1. Identify a point on the solid line: Look for a point on the parent function (solid line) and note its coordinates.

2. Identify the corresponding point on the dotted line: Look for the corresponding point on the translated function (dotted line) at the same \( x \)-coordinate.

3. Calculate the vertical shift: The value of \( k \) is simply the difference in the \( y \)-coordinates of these two points. Specifically, it can be calculated as: \[ k = y_{\text{dotted}} - y_{\text{solid}} \]

If you have specific points from the graph you're referencing, substitute those values in to find \( k \). If you can provide those points, I can help you compute the exact value of \( k \).