What kind of transformation converts the graph of f(x) = 3|x + 7| - 4 into the graph of g(x) = 3|x + 7| + 6? Choices: (A)translation 10 units right (B)translation 10 units left (C)translation 10 units down (D)translation 10 units up

Identify Function Structure: Identify the basic structure of the functions f(x) and g(x). Both functions have the same structure, with the absolute value of (x + 7) being multiplied by 3. The only difference is the constant term at the end of the functions.Determine Transformation Type: Determine the type of transformation based on the change in the constant term. The function f(x) has a constant term of -4, while the function g(x) has a constant term of +6. This indicates a vertical shift.Calculate Vertical Shift: Calculate the vertical shift required to transform f(x) into g(x). The difference in the constant terms is 6 - (-4) = 6 + 4 = 10. This means the graph of f(x) needs to be shifted up by 10 units to become the graph of g(x).Match Transformation to Choices: Match the calculated transformation to the given choices. The transformation is a vertical shift, and since we are moving the graph up, the correct choice is (D) translation 10 units up.

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What kind of transformation converts the graph of $f(x) = 3|x + 7| - 4$ into the graph of $g(x) = 3|x + 7| + 6$ ? $\newline$ Choices: $\newline$ (A) translation $10$ units right $\newline$ (B) translation $10$ units left $\newline$ (C) translation $10$ units down $\newline$ (D) translation $10$ units up

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Algebra 2

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = 3|x + 7| - 4

into the graph of

g(x) = 3|x + 7| + 6

\newline

Choices:

\newline

(A) translation

10

units right

\newline

(B) translation

10

units left

\newline

10

units down

\newline

(D) translation

10

units up

Identify Function Structure: Identify the basic structure of the functions $f(x)$ and $g(x)$ . Both functions have the same structure, with the absolute value of $(x + 7)$ being multiplied by $3$ . The only difference is the constant term at the end of the functions.
Determine Transformation Type: Determine the type of transformation based on the change in the constant term. $\newline$ The function $f(x)$ has a constant term of $-4$ , while the function $g(x)$ has a constant term of $+6$ . This indicates a vertical shift.
Calculate Vertical Shift: Calculate the vertical shift required to transform $f(x)$ into $g(x)$ . The difference in the constant terms is $6 - (-4) = 6 + 4 = 10$ . This means the graph of $f(x)$ needs to be shifted up by $10$ units to become the graph of $g(x)$ .
Match Transformation to Choices: Match the calculated transformation to the given choices. $\newline$ The transformation is a vertical shift, and since we are moving the graph up, the correct choice is $(D)$ translation $10$ units up.