What kind of transformation converts the graph of f(x) = -10|x + 6| - 5 into the graph of g(x) = -10|x + 6| + 3? Choices: (A)translation 8 units right (B)translation 8 units down (C)translation 8 units left (D)translation 8 units up

Analyze Functions: Analyze the given functions f(x) and g(x). f(x) = -10|x + 6| - 5 g(x) = -10|x + 6| + 3 Notice that the only difference between f(x) and g(x) is the constant term at the end of the equation.Type of Transformation: Determine the type of transformation. The change from -5 to +3 indicates a vertical shift because the absolute value expression, which affects the shape of the graph, remains unchanged.Calculate Shift Magnitude: Calculate the magnitude of the vertical shift. The constant term in f(x) is -5, and in g(x) it is +3. To find the shift, calculate the difference between these constants. Shift = 3 - (-5) = 3 + 5 = 8Direction of Shift: Determine the direction of the vertical shift. Since the constant term increased from -5 to +3, the graph of f(x) has been shifted upwards to become g(x).Match Transformation: Match the transformation with the given choices. The graph of f(x) has been shifted 8 units up to become the graph of g(x). This matches choice (D) translation 8 units up.

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What kind of transformation converts the graph of $f(x) = -10|x + 6| - 5$ into the graph of $g(x) = -10|x + 6| + 3$ ? $\newline$ Choices: $\newline$ (A) translation $8$ units right $\newline$ (B) translation $8$ units down $\newline$ (C) translation $8$ units left $\newline$ (D) translation $8$ 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) = -10|x + 6| - 5

into the graph of

g(x) = -10|x + 6| + 3

\newline

Choices:

\newline

(A) translation

8

units right

\newline

(B) translation

8

units down

\newline

8

units left

\newline

(D) translation

8

units up

Analyze Functions: Analyze the given functions $f(x)$ and $g(x)$ . $f(x) = -10|x + 6| - 5$ $g(x) = -10|x + 6| + 3$ Notice that the only difference between $f(x)$ and $g(x)$ is the constant term at the end of the equation.
Type of Transformation: Determine the type of transformation. $\newline$ The change from $-5$ to $+3$ indicates a vertical shift because the absolute value expression, which affects the shape of the graph, remains unchanged.
Calculate Shift Magnitude: Calculate the magnitude of the vertical shift. $\newline$ The constant term in $f(x)$ is $-5$ , and in $g(x)$ it is $+3$ . To find the shift, calculate the difference between these constants. $\newline$ Shift = $3 - (-5) = 3 + 5 = 8$
Direction of Shift: Determine the direction of the vertical shift. $\newline$ Since the constant term increased from $-5$ to $+3$ , the graph of $f(x)$ has been shifted upwards to become $g(x)$ .
Match Transformation: Match the transformation with the given choices. $\newline$ The graph of $f(x)$ has been shifted $8$ units up to become the graph of $g(x)$ . This matches choice (D) translation $8$ units up.