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=
Remaining Attempts : 3
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Answer 1

To determine the value of \( k \) for the translated function \( y = f(x) + k \), you need to observe how the solid line (the parent function) has been shifted vertically to obtain the dotted line (the translated function).

1. Identify a specific point on the parent function \( y = f(x) \). For example, find a coordinate point on the solid line.
2. Identify the corresponding point on the dotted line (the shifted version).
3. Calculate the vertical distance between these two points.

The value of \( k \) will be equal to this vertical distance.

If the dotted line is above the solid line, \( k \) is positive (indicating an upward shift), and if it is below, \( k \) is negative (indicating a downward shift).

Based on the graph, if you have specific y-values for a particular x-value from both lines, you can find \( k \) by using the formula:

\[ k = y_{dotted} - y_{solid} \]

Please check the specific values for \( y \) to find the value of \( k \). If you provide me with specific coordinates from the graph, I can help you calculate \( k \).