What does the transformation f(x) ↦ f(4x) do to the graph of f(x)? Choices: [[stretches it vertically][stretches it horizontally][shrinks it horizontally][shrinks it vertically]]

Horizontal Scaling Explanation: The transformation f(x) ↦ f(4x) affects the horizontal scaling of the graph of f(x). To understand the effect, consider a point (a, b) on the graph of f(x). After the transformation, this point will be mapped to (a/4, b) because f(4*(a/4)) = f(a) = b. This means that every x-coordinate is scaled by a factor of 1/4, which makes the graph ＂shrink＂ horizontally by a factor of 4. 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. 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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What does the transformation $f(x) \mapsto f(4x)$ do to the graph of $f(x)$ ? $\newline$ Choices: $\newline$ [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) \mapsto f(4x)

do to the graph of

f(x)

\newline

Choices:

\newline

[A] stretches it vertically

\newline

[B] stretches it horizontally

\newline

[C]shrinks it horizontally

\newline

[D]shrinks it vertically

Horizontal Scaling Explanation: The transformation $f(x) \mapsto f(4x)$ affects the horizontal scaling of the graph of $f(x)$ . To understand the effect, consider a point $(a, b)$ on the graph of $f(x)$ . After the transformation, this point will be mapped to $(\frac{a}{4}, b)$ because $f(4*(\frac{a}{4})) = f(a) = b$ . This means that every $x$ -coordinate is scaled by a factor of $\frac{1}{4}$ , which makes the graph ＂shrink＂ horizontally by a factor of $4$ .
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.
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.＂