What kind of transformation converts the graph of f(x) = -5|x + 7| - 2 into the graph of g(x) = -5|x + 7| - 6? Choices: (A)translation 4 units left (B)translation 4 units down (C)translation 4 units right (D)translation 4 units up

Identify Structure: Identify the structure of both functions. f(x) = -5|x + 7| - 2 and g(x) = -5|x + 7| - 6 are both in the form of y = a|x + b| + c, where a, b, and c are constants.Compare Constants: Compare the constants of both functions. The only difference between f(x) and g(x) is the constant term at the end of the equation. For f(x), it is -2, and for g(x), it is -6.Determine Transformation: Determine the type of transformation based on the change in the constant term. The change from -2 to -6 is a vertical shift because it affects the y-value directly. The absolute value part of the function, which affects the x-value, remains unchanged.Calculate Shift: Calculate the magnitude and direction of the vertical shift. The change from -2 to -6 is a decrease of 4 units in the y-value. This means the graph has moved down by 4 units.Match Transformation: Match the transformation to the given choices. The graph has been translated 4 units down, which corresponds to choice (B).

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What kind of transformation converts the graph of $f(x) = -5|x + 7| - 2$ into the graph of $g(x) = -5|x + 7| - 6$ ? $\newline$ Choices: $\newline$ (A) translation $4$ units left $\newline$ (B) translation $4$ units down $\newline$ (C) translation $4$ units right $\newline$ (D) translation $4$ units up

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Math Problems

Algebra 1

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = -5|x + 7| - 2

into the graph of

g(x) = -5|x + 7| - 6

\newline

Choices:

\newline

(A) translation

4

units left

\newline

(B) translation

4

units down

\newline

4

units right

\newline

(D) translation

4

units up

Identify Structure: Identify the structure of both functions. $\newline$ $f(x) = -5|x + 7| - 2$ and $g(x) = -5|x + 7| - 6$ are both in the form of $y = a|x + b| + c$ , where $a$ , $b$ , and $c$ are constants.
Compare Constants: Compare the constants of both functions. The only difference between $f(x)$ and $g(x)$ is the constant term at the end of the equation. For $f(x)$ , it is $-2$ , and for $g(x)$ , it is $-6$ .
Determine Transformation: Determine the type of transformation based on the change in the constant term. $\newline$ The change from $-2$ to $-6$ is a vertical shift because it affects the $y$ -value directly. The absolute value part of the function, which affects the $x$ -value, remains unchanged.
Calculate Shift: Calculate the magnitude and direction of the vertical shift. $\newline$ The change from $-2$ to $-6$ is a decrease of $4$ units in the $y$ -value. This means the graph has moved down by $4$ units.
Match Transformation: Match the transformation to the given choices. $\newline$ The graph has been translated $4$ units down, which corresponds to choice $(B)$ .