What kind of transformation converts the graph of f(x) = -3|x - 6| + 3 into the graph of g(x) = -3|x - 6| - 7? Choices: (A)translation 10 units left (B)translation 10 units down (C)translation 10 units up (D)translation 10 units right

Analyze Functions: Analyze the given functions to determine the type of transformation. We have f(x) = -3|x - 6| + 3 and g(x) = -3|x - 6| - 7. Both functions have the same coefficient and absolute value expression, but the constants at the end are different.Compare Constants: Compare the constants of f(x) and g(x). The constant term in f(x) is +3, and in g(x) it is -7. The change in the constant term indicates a vertical shift.Vertical Shift Determination: Determine the direction and magnitude of the vertical shift. The constant term decreased from +3 to -7, which is a decrease of 10 units. This means the graph has shifted 10 units vertically.Direction of Shift: Determine if the shift is upwards or downwards. Since the constant term decreased, the graph has shifted downwards.Match Transformation: Match the transformation with the given choices. The graph of f(x) has shifted 10 units downwards to become g(x). The correct choice is (B) translation 10 units down.

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What kind of transformation converts the graph of $f(x) = -3|x - 6| + 3$ into the graph of $g(x) = -3|x - 6| - 7$ ? $\newline$ Choices: $\newline$ (A) translation $10$ units left $\newline$ (B) translation $10$ units down $\newline$ (C) translation $10$ units up $\newline$ (D) translation $10$ units right

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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) = -3|x - 6| + 3

into the graph of

g(x) = -3|x - 6| - 7

\newline

Choices:

\newline

(A) translation

10

units left

\newline

(B) translation

10

units down

\newline

10

units up

\newline

(D) translation

10

units right

Analyze Functions: Analyze the given functions to determine the type of transformation. $\newline$ We have $f(x) = -3|x - 6| + 3$ and $g(x) = -3|x - 6| - 7$ . $\newline$ Both functions have the same coefficient and absolute value expression, but the constants at the end are different.
Compare Constants: Compare the constants of $f(x)$ and $g(x)$ . The constant term in $f(x)$ is $+3$ , and in $g(x)$ it is $-7$ . The change in the constant term indicates a vertical shift.
Vertical Shift Determination: Determine the direction and magnitude of the vertical shift. $\newline$ The constant term decreased from $+3$ to $-7$ , which is a decrease of $10$ units. $\newline$ This means the graph has shifted $10$ units vertically.
Direction of Shift: Determine if the shift is upwards or downwards. $\newline$ Since the constant term decreased, the graph has shifted downwards.
Match Transformation: Match the transformation with the given choices. $\newline$ The graph of $f(x)$ has shifted $10$ units downwards to become $g(x)$ . $\newline$ The correct choice is (B) translation $10$ units down.