The following ordered pairs come from a function transformation the original ordered pair is 2, 9 and the transformation ordered pair is 6, 9 which of the following correctly identifies the value of k in describes whether it is a compression or a stretch

Question

1/3 stretch
1/3 compression
Three stre
Three compression

Answer 1

To determine the value of $k$ and whether the transformation is a compression or a stretch, we can analyze the given ordered pairs.

The original ordered pair is $(2,9)$ and the transformed ordered pair is $(6,9)$. From this, we can see that the y-coordinates remain the same (both are 9), while the x-coordinates change from 2 to 6.

This transformation affects the x-coordinate. We can conceptualize this transformation as changing $x$ by a factor of $k$:

$$k=\frac{\text{New }x}{\text{Original }x}=\frac{6}{2}=3$$

Since the value of $k$ is greater than 1, it indicates a stretch in the x-direction. In general, a stretch occurs when $k>1$ and a compression occurs when $k<1$.

Based on the options provided, the correct identification would be:

• $k=3$
• This is a stretch.

So the answer is Three stretch.