To determine the value of \( k \) in the translated function, we need to identify the vertical shift applied to the parent function \( f(x) = |x| \).
If the translated function is in the form \( f(x) = |x| + k \), the value of \( k \) represents a vertical shift:
- If \( k > 0 \), the graph is shifted upwards by \( k \) units.
- If \( k < 0 \), the graph is shifted downwards by \( |k| \) units.
To find the specific value of \( k \), you would typically look at the point where the solid line (the parent function) and the dotted line (the translated function) intersect or the specific shift shown in the vertical direction on the graph.
Since we do not have access to the image, if the translated function is clearly above or below the parent function, that would help to determine the precise value of \( k \).
For example:
- If the entire graph of the dotted translated function is 3 units above the solid parent function, then \( k = 3 \).
- If the dotted graph is 2 units below the solid graph, then \( k = -2 \).
Without the specific visual information, you would determine \( k \) based on the visual distance between the two lines in the graph given. Please look at the graph to see how far the dotted line is shifted from the solid line to find your answer. The final answer format should be:
The value of \( k \) in the translated function is \( f(x) = |x| + k \).