What kind of transformation converts the graph of f(x) = 9|x + 6| - 4 into the graph of g(x) = 9|x + 6| - 9? Choices: (A)translation 5 units up (B)translation 5 units left (C)translation 5 units down (D)translation 5 units right

Identify Transformation: Identify the transformation between f(x) and g(x) by comparing the two functions. The function f(x) = 9|x + 6| - 4 is being transformed into g(x) = 9|x + 6| - 9. The only difference between these two functions is the constant term at the end of the expression. Since the constant term in f(x) is -4 and in g(x) it is -9, the transformation involves a vertical shift.Determine Vertical Shift: Determine the direction and magnitude of the vertical shift. The constant term in f(x) has decreased by 5 units to become the constant term in g(x) (from -4 to -9). This indicates a vertical shift downward by 5 units.Match Transformation: Match the transformation to the given choices. The transformation is a translation 5 units down, which corresponds to choice (C).

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What kind of transformation converts the graph of $f(x) = 9|x + 6| - 4$ into the graph of $g(x) = 9|x + 6| - 9$ ? $\newline$ Choices: $\newline$ (A) translation $5$ units up $\newline$ (B) translation $5$ units left $\newline$ (C) translation $5$ units down $\newline$ (D) translation $5$ units right

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Math Problems

Algebra 2

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = 9|x + 6| - 4

into the graph of

g(x) = 9|x + 6| - 9

\newline

Choices:

\newline

(A) translation

5

units up

\newline

(B) translation

5

units left

\newline

5

units down

\newline

(D) translation

5

units right

Identify Transformation: Identify the transformation between $f(x)$ and $g(x)$ by comparing the two functions. $\newline$ The function $f(x) = 9|x + 6| - 4$ is being transformed into $g(x) = 9|x + 6| - 9$ . The only difference between these two functions is the constant term at the end of the expression. Since the constant term in $f(x)$ is $-4$ and in $g(x)$ it is $-9$ , the transformation involves a vertical shift.
Determine Vertical Shift: Determine the direction and magnitude of the vertical shift. The constant term in $f(x)$ has decreased by $5$ units to become the constant term in $g(x)$ (from $-4$ to $-9$ ). This indicates a vertical shift downward by $5$ units.
Match Transformation: Match the transformation to the given choices. $\newline$ The transformation is a translation $5$ units down, which corresponds to choice $(C)$ .