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What does the transformation f(x)↦f(4x) f(x) \mapsto f(4x) do to the graph of f(x) f(x) ?\newlineChoices:\newline[A] stretches it vertically\newline[B] stretches it horizontally\newline[C]shrinks it horizontally\newline[D]shrinks it vertically

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Q. What does the transformation f(x)↦f(4x) f(x) \mapsto f(4x) do to the graph of f(x) f(x) ?\newlineChoices:\newline[A] stretches it vertically\newline[B] stretches it horizontally\newline[C]shrinks it horizontally\newline[D]shrinks it vertically
  1. Horizontal Scaling Explanation: The transformation f(x)↦f(4x)f(x) \mapsto f(4x) affects the horizontal scaling of the graph of f(x)f(x). To understand the effect, consider a point (a,b)(a, b) on the graph of f(x)f(x). After the transformation, this point will be mapped to (a4,b)(\frac{a}{4}, b) because f(4∗(a4))=f(a)=bf(4*(\frac{a}{4})) = f(a) = b. This means that every xx-coordinate is scaled by a factor of 14\frac{1}{4}, which makes the graph ＂shrink＂ horizontally by a factor of 44.
  2. Elimination of Vertical Changes: Since the graph is shrinking horizontally, we can eliminate the options that suggest a vertical change (stretching or shrinking vertically). This leaves us with the choices that involve horizontal changes.
  3. Selection of Horizontal Shrink: Between the two remaining options, ＂stretches it horizontally＂ and ＂shrinks it horizontally,＂ we have already established that the transformation causes a horizontal shrink, not a stretch. Therefore, the correct choice is ＂shrinks it horizontally.＂

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