Question

One graph there are 2 curved lines the original has points (0,0), (1,1)
The transformed graph has points (0,0), 1,1/4)
Identify the k value
2
1/4
1/2
4

Answer 1

To find the value of \( k \) for the transformed graph given the original and transformed points, we need to observe how the transformation affects the coordinates.

The original graph passes through the points \( (0,0) \) and \( (1,1) \). The transformed graph passes through the points \( (0,0) \) and \( (1, \frac{1}{4}) \).

This suggests that the transformation affects the \( y \)-coordinates. If we denote the original function as \( f(x) \) and the transformed function as \( g(x) \), we can observe:

1. At \( x = 1 \):
\[
f(1) = 1 \quad \text{(original point)}
\]
\[
g(1) = \frac{1}{4} \quad \text{(transformed point)}
\]

Now, we can express the transformation as:
\[
g(x) = k \cdot f(x)
\]

Substituting the points into this equation gives:
\[
g(1) = k \cdot f(1)
\]
\[
\frac{1}{4} = k \cdot 1
\]

From this, we can solve for \( k \):
\[
k = \frac{1}{4}
\]

Therefore, the value of \( k \) is \( \frac{1}{4} \).