Question

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 \( k \) representing the vertical shift in the function \( y = f(x) + k \), you need to identify the vertical distance between the solid line (the parent function \( y = f(x) \)) and the dotted line (the translated form \( y = f(x) + k \)).

1. If you can visually inspect the graph:
- Find a point on the solid line \( y = f(x) \) at a specific \( x \) value (let's say \( x = a \)).
- Note the corresponding \( y \) value, which we can call \( f(a) \).
- Then, find the same \( x \) value on the dotted line \( y = f(x) + k \) and note the new \( y \) value, which we can call \( g(a) \).

2. The relationship between these two points can be expressed as:
\[
g(a) = f(a) + k
\]

3. Rearranging the equation gives:
\[
k = g(a) - f(a)
\]

4. Therefore, the value of \( k \) is the vertical distance between the two lines for the same \( x \).

Please refer to the specific values on the graph to compute \( k \). If you provide the values or describe the points, I can help you compute \( k \).