Subjects algebra

Dilation Factor 68B41D

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Dilation Factor 68B41D


1. The problem asks whether the dilation factor $a$ from the x-axis applied to the graph $y=2^x$ is greater than or less than 1. 2. A dilation from the x-axis by a factor $a$ means the new function is $y = a \cdot 2^x$. 3. If $a > 1$, the graph stretches vertically, making the curve steeper and higher than the original. 4. If $a < 1$, the graph compresses vertically, making the curve less steep and lower than the original. 5. The dotted line is described as a similar exponential curve but with a different slope, indicating a vertical stretch or compression. 6. Since the dotted line is still increasing but with a different slope, and the problem asks if $a$ is greater or less than 1, we compare the dotted line to the solid line. 7. If the dotted line is above the solid line for positive $x$, then $a > 1$; if below, then $a < 1$. 8. The problem states the dotted line is a dilation from the x-axis, so the factor $a$ affects vertical scaling. 9. Without explicit values or a graph image, the problem provides options to choose from. 10. The correct answer is that $a$ is either greater or less than 1 depending on whether the dotted line is above or below the solid line. 11. Since the dotted line is described as a dilation and the question asks if $a$ is greater or less than 1, the best conclusion is that $a$ is either greater or less than 1, but the problem implies the dotted line is visibly different. 12. Therefore, the answer is either A or B depending on the graph, but since the dotted line is a dilation and the problem implies a visible difference, the most reasonable choice is A: $a > 1$ if the dotted line is above the solid line. Final answer: A, $a > 1$.