The transformation you mentioned indicates that the function is stretched or compressed based on the change in the coefficient of \(x\).
The original function is \(f(x) = 4x - 5\), and you have transformed it to \(42x - 5\).
To identify the value of \(k\) and whether it is a stretch or compression:
- In the original function, the coefficient of \(x\) is 4.
- In the transformed function, the coefficient of \(x\) is 42.
The relationship between the coefficients tells us about the transformation:
- If \(k > 1\), it is a stretch.
- If \(0 < k < 1\), it is a compression.
In this case, since \(42 > 4\), we can say that the graph is stretched.
- The value of \(k\) can be identified as the ratio of new coefficient over the old coefficient, which is \(k = \frac{42}{4} = 10.5\).
Thus, the specific value of \(k\) is 10.5, and the graph shows a stretch.
Based on your provided options, none of them state \(10.5\), but the correct responses from the choices would be:
- 2x; stretch (assuming this was meant to indicate a stretch, even though the numerical value is incorrect).
- 2; stretch (but \(2\) doesn't relate to \(k\) defined based on provided info either).
If you need to specify correctly based on the transformations and no exact value is listed, please clarify. The correct interpretation is that it is a stretch, but the exact response matches was not provided with \(10.5\).
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