What kind of transformation converts the graph of f(x) = 8(x + 3)^2 - 4 into the graph of g(x) = 8(x + 3)^2 - 8? Choices: (A)translation 4 units right (B)translation 4 units left (C)translation 4 units down (D)translation 4 units up

Identify Transformation Type: Identify the type of transformation based on the change in the functions. Compare f(x) = 8(x + 3)^2 - 4 with g(x) = 8(x + 3)^2 - 8. Notice that the only change is in the constant term at the end of the function.Determine Transformation Direction: Determine the direction of the transformation. Since the change is in the constant term, and it is a subtraction (from -4 to -8), this indicates a vertical shift.Calculate Shift Magnitude: Calculate the magnitude of the vertical shift. The change in the constant term is from -4 to -8, which is a decrease of 4 units.Determine Shift Direction: Determine if the shift is upwards or downwards. Since the constant term decreased by 4 units, the graph shifts 4 units downwards.Match Transformation with Choices: Match the transformation with the given choices. The graph of f(x) shifts 4 units down to become the graph of g(x).

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What kind of transformation converts the graph of $f(x) = 8(x + 3)^2 - 4$ into the graph of $g(x) = 8(x + 3)^2 - 8$ ? $\newline$ Choices: $\newline$ (A) translation $4$ units right $\newline$ (B) translation $4$ units left $\newline$ (C) translation $4$ units down $\newline$ (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) = 8(x + 3)^2 - 4

into the graph of

g(x) = 8(x + 3)^2 - 8

\newline

Choices:

\newline

(A) translation

4

units right

\newline

(B) translation

4

units left

\newline

4

units down

\newline

(D) translation

4

units up

Identify Transformation Type: Identify the type of transformation based on the change in the functions. $\newline$ Compare $f(x) = 8(x + 3)^2 - 4$ with $g(x) = 8(x + 3)^2 - 8$ . $\newline$ Notice that the only change is in the constant term at the end of the function.
Determine Transformation Direction: Determine the direction of the transformation. Since the change is in the constant term, and it is a subtraction (from $-4$ to $-8$ ), this indicates a vertical shift.
Calculate Shift Magnitude: Calculate the magnitude of the vertical shift. The change in the constant term is from $-4$ to $-8$ , which is a decrease of $4$ units.
Determine Shift Direction: Determine if the shift is upwards or downwards. $\newline$ Since the constant term decreased by $4$ units, the graph shifts $4$ units downwards.
Match Transformation with Choices: Match the transformation with the given choices. $\newline$ The graph of $f(x)$ shifts $4$ units down to become the graph of $g(x)$ .