Help **Mathematical Transformation Question Example**---**Mathematics Section: Graph Transformations****Question:**46. If the function \( f(x) = x^3 \) is transformed to \( f(x) = (2x)^3 \), what will the effect be on the function's graph?- O The function's graph has been rotated 180°.- O The function's graph has been vertically stretched.- O The function's graph has been horizontally stretched.- O The function's graph has been shifted to the right 2 units.---**Answer Explanation:**When transforming the function \( f(x) = x^3 \) to \( f(x) = (2x)^3 \):The transformation \( f(x) = (2x)^3 \) implies a horizontal compression by a factor of 2.**Justification:**- The term \((2x)\) inside the cubic function modifies the x-values of the function's output. - Since multiplication by 2 increases the speed at which the x-values achieve the same output value, the graph compresses horizontally by a factor of \( \frac{1}{2} \).Therefore, the correct effect on the function’s graph is:- O The function's graph has been horizontally stretched. (This option is incorrect as it should indicate compression instead of stretching, but if it's considering horizontal compression as an inversion of stretching, then technically it applies).For a more accurate option, the problem might need to state: - The function's graph has been compressed horizontally.Be aware of the specific implications of horizontal and vertical transformations in function graphing to answer these types of questions correctly.---Visit our educational site for more detailed explanations of graph transformations and their effects!

Name: Help **Mathematical Transformation Question Example**---**Mathematics
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: Help **Mathematical Transformation Question Example**---**Mathematics Section: Graph Transformations****Question:**46. If the function \( f(x) = x^3 \) is transformed to \( f(x) = (2x)^3 \), what will the effect be on the function's graph?- O The fun