What kind of transformation converts the graph of f(x) = 5(x - 5)^2 - 6 into the graph of g(x) = 5(x - 10)^2 - 6? Choices: (A)translation 5 units down (B)translation 5 units up (C)translation 5 units left (D)translation 5 units right

Compare Functions: To determine the type of transformation, we need to compare the two functions f(x) and g(x) and see how the graph of f(x) has been altered to become the graph of g(x).Original and Transformed Functions: The original function is f(x) = 5(x - 5)^2 - 6. The transformed function is g(x) = 5(x - 10)^2 - 6. We notice that the only change is in the expression inside the parentheses: (x - 5) has become (x - 10).Identify Horizontal Shift: The change from (x - 5) to (x - 10) indicates a horizontal shift. Since the number inside the parentheses has increased from 5 to 10, this means the graph has been shifted to the right.Calculate Shift Amount: The amount of the shift is the difference between the two numbers inside the parentheses, which is 10 - 5 = 5 units. Therefore, the graph has been translated 5 units to the right.

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What kind of transformation converts the graph of $f(x) = 5(x - 5)^2 - 6$ into the graph of $g(x) = 5(x - 10)^2 - 6$ ? $\newline$ Choices: $\newline$ (A) translation $5$ units down $\newline$ (B) translation $5$ units up $\newline$ (C) translation $5$ units left $\newline$ (D) translation $5$ units right

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Precalculus

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = 5(x - 5)^2 - 6

into the graph of

g(x) = 5(x - 10)^2 - 6

\newline

Choices:

\newline

(A) translation

5

units down

\newline

(B) translation

5

units up

\newline

5

units left

\newline

(D) translation

5

units right

Compare Functions: To determine the type of transformation, we need to compare the two functions $f(x)$ and $g(x)$ and see how the graph of $f(x)$ has been altered to become the graph of $g(x)$ .
Original and Transformed Functions: The original function is $f(x) = 5(x - 5)^2 - 6$ . The transformed function is $g(x) = 5(x - 10)^2 - 6$ . We notice that the only change is in the expression inside the parentheses: $(x - 5)$ has become $(x - 10)$ .
Identify Horizontal Shift: The change from $(x - 5)$ to $(x - 10)$ indicates a horizontal shift. Since the number inside the parentheses has increased from $5$ to $10$ , this means the graph has been shifted to the right.
Calculate Shift Amount: The amount of the shift is the difference between the two numbers inside the parentheses, which is $10 - 5 = 5$ units. Therefore, the graph has been translated $5$ units to the right.