Question

The equation f(x)=4x−5
is transformed to 42x−5
. Identify the value of k. Does the graph show a stretch or a compression?(1 point)
Responses

2; compression
2; compression

2x
; stretch
2 x ; stretch

2x
; compression
2 x ; compression

2; stretch

Answer 1

To analyze the transformation of the function \( f(x) = 4x - 5 \) to \( f(x) = 42x - 5 \), we need to focus on the coefficient of \( x \) in each function.

1. The original function is \( f(x) = 4x - 5 \), where the coefficient of \( x \) (denoted as \( k \)) is 4.
2. The transformed function is \( f(x) = 42x - 5 \), where the new coefficient of \( x \) is 42.

To find the value of \( k \), we can express how the coefficient has changed:
\[
k = \frac{\text{new coefficient}}{\text{original coefficient}} = \frac{42}{4} = 10.5
\]

Upon evaluating this, it looks like a misunderstanding might have occurred since the possible responses gave the value of \( k \) as 2, which doesn't match what we calculated.

### Stretch or Compression?
The transformation results in a larger coefficient (from 4 to 42), indicating a vertical stretch. When the coefficient of \( x \) increases, the graph stretches away from the x-axis.

### Conclusion:
- Assuming a possible misinterpretation of the question's options, we can reasonably say:
- \( k = 10.5 \), but if it needs to fit a choice, it seems an error occurred.
- **The graph indicates a stretch.**

If only 2 was among the choices assuming it was presented, then:
- **Response**: 2; stretch. (This would align with label options, even if it’s not mathematically the exact coefficient we calculated.)

However, based on the calculated transformation, the resulting \( k \) should be explicitly noted as 10.5 for accuracy.