What kind of transformation converts the graph of f(x) = -10(x + 10)^2 - 9 into the graph of g(x) = -10(x + 10)^2 - 8? Choices: (A)translation 1 unit down (B)translation 1 unit right (C)translation 1 unit left (D)translation 1 unit up

Analyze Functions: Analyze the given functions to determine the type of transformation. The given functions are f(x) = -10(x + 10)^2 - 9 and g(x) = -10(x + 10)^2 - 8. We need to compare these two functions to understand how g(x) is obtained from f(x).Compare Y-Values: Compare the y-values of the functions. The only difference between f(x) and g(x) is the constant term at the end of the equation. f(x) has a constant term of -9, while g(x) has a constant term of -8.Determine Shift Direction: Determine the direction of the shift. Since the constant term in g(x) is one unit greater than the constant term in f(x), this indicates a vertical shift upwards by 1 unit.Match Transformation: Match the transformation with the given choices. The transformation is a vertical shift, so it cannot be a translation to the left or right. Between the two remaining choices, translation 1 unit down or translation 1 unit up, we have determined that the shift is upwards. Therefore, the correct choice is translation 1 unit up.

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What kind of transformation converts the graph of $f(x) = -10(x + 10)^2 - 9$ into the graph of $g(x) = -10(x + 10)^2 - 8$ ? $\newline$ Choices: $\newline$ (A) translation $1$ unit down $\newline$ (B) translation $1$ unit right $\newline$ (C) translation $1$ unit left $\newline$ (D) translation $1$ unit up

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Algebra 1

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = -10(x + 10)^2 - 9

into the graph of

g(x) = -10(x + 10)^2 - 8

\newline

Choices:

\newline

(A) translation

1

unit down

\newline

(B) translation

1

unit right

\newline

1

unit left

\newline

(D) translation

1

unit up

Analyze Functions: Analyze the given functions to determine the type of transformation. $\newline$ The given functions are $f(x) = -10(x + 10)^2 - 9$ and $g(x) = -10(x + 10)^2 - 8$ . We need to compare these two functions to understand how $g(x)$ is obtained from $f(x)$ .
Compare Y-Values: Compare the y-values of 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 a constant term of $-9$ , while $g(x)$ has a constant term of $-8$ .
Determine Shift Direction: Determine the direction of the shift. $\newline$ Since the constant term in $g(x)$ is one unit greater than the constant term in $f(x)$ , this indicates a vertical shift upwards by $1$ unit.
Match Transformation: Match the transformation with the given choices. $\newline$ The transformation is a vertical shift, so it cannot be a translation to the left or right. Between the two remaining choices, translation $1$ unit down or translation $1$ unit up, we have determined that the shift is upwards. Therefore, the correct choice is translation $1$ unit up.