Question

The graph of y=log_10 ​x is translated in the positive y-direction by 2 units. This translation is equivalent to a stretch of factor k parallel to the x-axis. What is the value of k ?

Answer 1

The value of k (the stretch factor) is 100.



Steps to Solve:

Analyze the Original Graph:

y = log_10(x) has a characteristic shape with the y-intercept at (1, 0).

Translate 2 Units Up:

The new equation becomes y = log_10(x) + 2, shifting the y-intercept to (1, 2).

Determine Equivalent Stretch Factor:

To achieve the same y-value of 2 at x = 1 using a stretch, we need a factor that "slows down" the original graph's growth.

This means stretching it horizontally, making it wider.

The correct stretch factor is 10^2 = 100.

FINAL ANSWER:

The value of k (the stretch factor) is 100.



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