What kind of transformation converts the graph of f(x) = 9|x + 6| - 9 into the graph of g(x) = 9|x + 6| + 1? Choices: (A)translation 10 units right (B)translation 10 units up (C)translation 10 units down (D)translation 10 units left

Analyze Functions: Analyze the given functions. We have f(x) = 9|x + 6| - 9 and g(x) = 9|x + 6| + 1. Compare the two functions to determine the type of transformation.Identify Difference: 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 +1.Direction of Transformation: Determine the direction of the transformation. Since the change is in the constant term, this indicates a vertical shift.Calculate Shift Amount: Calculate the amount of vertical shift. The change from -9 to +1 is an increase of 10 units. To find the shift, we calculate 1 - (-9) = 1 + 9 = 10.Type of Vertical Shift: Determine the type of vertical shift. Since the constant term increased by 10, the graph of f(x) is shifted 10 units up to become g(x).

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What kind of transformation converts the graph of $f(x) = 9|x + 6| - 9$ into the graph of $g(x) = 9|x + 6| + 1$ ? $\newline$ Choices: $\newline$ (A) translation $10$ units right $\newline$ (B) translation $10$ units up $\newline$ (C) translation $10$ units down $\newline$ (D) translation $10$ units left

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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) = 9|x + 6| - 9

into the graph of

g(x) = 9|x + 6| + 1

\newline

Choices:

\newline

(A) translation

10

units right

\newline

(B) translation

10

units up

\newline

10

units down

\newline

(D) translation

10

units left

Analyze Functions: Analyze the given functions. $\newline$ We have $f(x) = 9|x + 6| - 9$ and $g(x) = 9|x + 6| + 1$ . $\newline$ Compare the two functions to determine the type of transformation.
Identify Difference: 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. $\newline$ $f(x)$ has $-9$ , and $g(x)$ has $+1$ .
Direction of Transformation: Determine the direction of the transformation. Since the change is in the constant term, this indicates a vertical shift.
Calculate Shift Amount: Calculate the amount of vertical shift. $\newline$ The change from $-9$ to $+1$ is an increase of $10$ units. $\newline$ To find the shift, we calculate $1 - (-9) = 1 + 9 = 10$ .
Type of Vertical Shift: Determine the type of vertical shift. $\newline$ Since the constant term increased by $10$ , the graph of $f(x)$ is shifted $10$ units up to become $g(x)$ .