What kind of transformation converts the graph of f(x) = 4|x + 9| + 3 into the graph of g(x) = 4|x + 7| + 3? Choices: (A)translation 2 units right (B)translation 2 units up (C)translation 2 units left (D)translation 2 units down

Compare Expressions: To determine the type of transformation, we need to compare the expressions inside the absolute value function of f(x) and g(x). In f(x), the expression is |x + 9|, and in g(x), it is |x + 7|. We can see that the number inside the absolute value has decreased by 2, going from +9 to +7.Horizontal Shift: This decrease by 2 inside the absolute value function indicates a horizontal shift. Since the value inside the absolute value has decreased, the graph has moved to the right. A decrease inside the absolute value corresponds to a rightward shift of the graph.Vertical Component: The vertical component of the function, which is outside the absolute value, has not changed. It remains +3 in both f(x) and g(x). This means there is no vertical shift.Overall Transformation: Therefore, the transformation that converts the graph of f(x) = 4|x + 9| + 3 into the graph of g(x) = 4|x + 7| + 3 is a translation 2 units to the right.

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What kind of transformation converts the graph of $f(x) = 4|x + 9| + 3$ into the graph of $g(x) = 4|x + 7| + 3$ ? $\newline$ Choices: $\newline$ (A) translation $2$ units right $\newline$ (B) translation $2$ units up $\newline$ (C) translation $2$ units left $\newline$ (D) translation $2$ units down

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Precalculus

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = 4|x + 9| + 3

into the graph of

g(x) = 4|x + 7| + 3

\newline

Choices:

\newline

(A) translation

2

units right

\newline

(B) translation

2

units up

\newline

2

units left

\newline

(D) translation

2

units down

Compare Expressions: To determine the type of transformation, we need to compare the expressions inside the absolute value function of $f(x)$ and $g(x)$ . In $f(x)$ , the expression is $|x + 9|$ , and in $g(x)$ , it is $|x + 7|$ . We can see that the number inside the absolute value has decreased by $2$ , going from $+9$ to $+7$ .
Horizontal Shift: This decrease by $2$ inside the absolute value function indicates a horizontal shift. Since the value inside the absolute value has decreased, the graph has moved to the right. A decrease inside the absolute value corresponds to a rightward shift of the graph.
Vertical Component: The vertical component of the function, which is outside the absolute value, has not changed. It remains $+3$ in both $f(x)$ and $g(x)$ . This means there is no vertical shift.
Overall Transformation: Therefore, the transformation that converts the graph of $f(x) = 4|x + 9| + 3$ into the graph of $g(x) = 4|x + 7| + 3$ is a translation $2$ units to the right.