What kind of transformation converts the graph of f(x) = -4(x + 8)^2 - 9 into the graph of g(x) = -4(x + 8)^2 - 7? Choices: (A)translation 2 units down (B)translation 2 units left (C)translation 2 units right (D)translation 2 units up

Analyze Functions: Analyze the given functions. We have f(x) = -4(x + 8)^2 - 9 and g(x) = -4(x + 8)^2 - 7. Compare the two functions to determine the type of transformation.Identify Change: Identify the change in the functions. The only difference between f(x) and g(x) is the constant term at the end of the equation. f(x) has -9, and g(x) has -7.Determine Transformation Direction: Determine the direction of the transformation. Since the change is in the constant term, and it is from -9 to -7, this indicates a vertical shift. The graph is moving up because the y-value at every x is increasing by 2.Calculate Transformation Magnitude: Calculate the magnitude of the transformation. The change in the constant term is from -9 to -7, which is an increase of 2 units. Therefore, the graph of f(x) is translated 2 units up to become g(x).

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What kind of transformation converts the graph of $f(x) = -4(x + 8)^2 - 9$ into the graph of $g(x) = -4(x + 8)^2 - 7$ ? $\newline$ Choices: $\newline$ (A) translation $2$ units down $\newline$ (B) translation $2$ units left $\newline$ (C) translation $2$ units right $\newline$ (D) translation $2$ 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) = -4(x + 8)^2 - 9

into the graph of

g(x) = -4(x + 8)^2 - 7

\newline

Choices:

\newline

(A) translation

2

units down

\newline

(B) translation

2

units left

\newline

2

units right

\newline

(D) translation

2

units up

Analyze Functions: Analyze the given functions. $\newline$ We have $f(x) = -4(x + 8)^2 - 9$ and $g(x) = -4(x + 8)^2 - 7$ . Compare the two functions to determine the type of transformation.
Identify Change: Identify the change in the functions. $\newline$ The only difference between $f(x)$ and $g(x)$ is the constant term at the end of the equation. $f(x)$ has $-9$ , and $g(x)$ has $-7$ .
Determine Transformation Direction: Determine the direction of the transformation. $\newline$ Since the change is in the constant term, and it is from $-9$ to $-7$ , this indicates a vertical shift. The graph is moving up because the $y$ -value at every $x$ is increasing by $2$ .
Calculate Transformation Magnitude: Calculate the magnitude of the transformation. $\newline$ The change in the constant term is from $-9$ to $-7$ , which is an increase of $2$ units. Therefore, the graph of $f(x)$ is translated $2$ units up to become $g(x)$ .