To analyze the transformation from \( f(x) = 4x - 5 \) to \( 42x - 5 \), we can first express the functions as \( f(x) = 4x - 5 \) and \( g(x) = 42x - 5 \).
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Identify the coefficient of \( x \) in each function:
- In \( f(x) = 4x - 5 \), the coefficient of \( x \) is \( 4 \).
- In \( g(x) = 42x - 5 \), the coefficient of \( x \) is \( 42 \).
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To see how the transformation affects the graph, we can calculate the factor by which the function has been stretched or compressed:
- The factor is given by \( \frac{42}{4} = 10.5 \).
Since the factor is greater than 1 (\( 10.5 \)), it indicates that the graph of the function has undergone a stretch.
Regarding value \( k \), in this case, \( k = \frac{42}{4} = 10.5 \).
So, the final answer is:
- \( k = 10.5 \); and the graph shows a stretch.
Therefore, the appropriate response would be: 10.5 ; stretch