The curve with equation undergoes a transformation: first a stretch by factor parallel to the -axis, followed by a translation of units in the negative -direction. What is the equation of the resulting curve?
Answer and explanation
Correct answer: A.
- Step 1: A horizontal stretch by factor 2 parallel to the -axis scales the input variable, replacing with to give .
- Step 2: A subsequent translation of 3 units in the negative -direction replaces every occurrence of with , resulting in .
Answer
.
Why not the others: The form uses a compression factor of rather than a stretch factor of 2; the form applies translation before horizontal stretching; the form combines horizontal compression with nested translation.
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