Question

The following ordered pairs came from a function transformation the original ordered pair is 8, 2 and the transformation ordered pair is 2,2identify the value of k

Answer 1

To identify the value of \( k \) in the function transformation, we need to determine what kind of transformation has occurred between the original ordered pair \((8, 2)\) and the transformed ordered pair \((2, 2)\).

The original ordered pair indicates that \( f(8) = 2 \), and the transformed ordered pair indicates \( g(2) = 2 \).

From the information given, it seems that the transformation involves changing the input from \( 8 \) to \( 2 \) while keeping the output constant at \( 2 \).

One way to describe this transformation in terms of a function is by a horizontal compression or some form of adjustment to the input. If we denote the transformation as \( g(x) = f(kx) \), we can see that \( 2 = k \cdot 8\), which gives us:

\[
2 = k \cdot 8
\]

To solve for \( k \), we can rearrange the equation:

\[
k = \frac{2}{8} = \frac{1}{4}
\]

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