What does the transformation f(x) ↦ f(x – 4) do to the graph of f(x)? Choices: [[translates it 4 units right][translates it 4 units down][translates it 4 units left][translates it 4 units up]]

Given Transformation: We are given the transformation f(x) ↦ f(x – 4). We need to determine how this transformation affects the graph of the original function f(x).Recognition of Horizontal Shift: Recognize that the transformation involves the input variable x. The transformation f(x) ↦ f(x – 4) indicates a horizontal shift, as it changes the x-value at which a particular y-value of the function is obtained.Direction of Horizontal Shift: Determine the direction of the horizontal shift. In the transformation f(x) ↦ f(x – 4), the x-value is being reduced by 4 before being input into the function. This means that every point on the graph of f(x) will be shifted to the right by 4 units to compensate for this reduction.Confirmation of Vertical Shift: Confirm that the transformation does not involve any vertical shift, as there is no addition or subtraction outside the function f(x). Therefore, there is no translation up or down.

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What does the transformation $f(x) \mapsto f(x - 4)$ do to the graph of $f(x)$ ? $\newline$ Choices: $\newline$ (A) $\text{translates it } 4 \text{ units right}$ $\newline$ (B) $\text{translates it } 4 \text{ units down}$ $\newline$ (C) $\text{translates it } 4 \text{ units left}$ $\newline$ (D) $\text{translates it } 4 \text{ units up}$

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Algebra 2

Function transformation rules

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Q. What does the transformation

f(x) \mapsto f(x - 4)

do to the graph of

f(x)

\newline

Choices:

\newline

(A)

\text{translates it } 4 \text{ units right}

\newline

(B)

\text{translates it } 4 \text{ units down}

\newline

(C)

\text{translates it } 4 \text{ units left}

\newline

(D)

\text{translates it } 4 \text{ units up}

Given Transformation: We are given the transformation $f(x) \mapsto f(x - 4)$ . We need to determine how this transformation affects the graph of the original function $f(x)$ .
Recognition of Horizontal Shift: Recognize that the transformation involves the input variable $x$ . The transformation $f(x) \mapsto f(x - 4)$ indicates a horizontal shift, as it changes the $x$ -value at which a particular $y$ -value of the function is obtained.
Direction of Horizontal Shift: Determine the direction of the horizontal shift. In the transformation $f(x) \mapsto f(x - 4)$ , the $x$ -value is being reduced by $4$ before being input into the function. This means that every point on the graph of $f(x)$ will be shifted to the right by $4$ units to compensate for this reduction.
Confirmation of Vertical Shift: Confirm that the transformation does not involve any vertical shift, as there is no addition or subtraction outside the function $f(x)$ . Therefore, there is no translation up or down.