The graph shows a parent function y=f(x)

Question

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

(1 point)
k=
𝑘
=

Answer 1

To determine the value of \( k \) in the transformation \( y = f(x) + k \), you need to analyze the vertical shift between the solid line \( y = f(x) \) and the dotted line \( y = f(x) + k \).

Here's how to find \( k \):

1. Identify a point on the solid line \( y = f(x) \). Let's say this point is \( (x_0, y_0) \).
2. Find the corresponding point on the dotted line \( y = f(x) + k \). This point will have the same \( x \)-coordinate but a different \( y \)-coordinate, \( (x_0, y_0 + k) \).
3. Determine the vertical distance between the two points. This distance is \( k \).
   • If the dotted line is above the solid line, then \( k \) is positive.
   • If the dotted line is below the solid line, then \( k \) is negative.

If you provide specific coordinates from the graph or more context from the graph itself, I could help you calculate the exact value of \( k \).

Answer 2

Answer