What kind of transformation converts the graph of f(x) = 8|x + 8| + 5 into the graph of g(x) = 8|x + 7| + 5? Choices: (A)translation 1 unit left (B)translation 1 unit up (C)translation 1 unit down (D)translation 1 unit right

Analyze Functions: Analyze the given functions. We have f(x) = 8|x + 8| + 5 and g(x) = 8|x + 7| + 5. We need to determine how the graph of f(x) is transformed to get the graph of g(x).Compare Absolute Value: Compare the inside of the absolute value. The only difference between f(x) and g(x) is the expression inside the absolute value. For f(x), it is |x + 8|, and for g(x), it is |x + 7|.Determine Horizontal Shift: Determine the horizontal shift. The expression inside the absolute value for g(x) is x + 7, which is x + 8 - 1. This indicates a horizontal shift of 1 unit to the left.Verify Vertical Shift: Verify that there is no vertical shift. The ＂+ 5＂ outside the absolute value in both f(x) and g(x) remains unchanged, which means there is no vertical shift.Conclude Transformation: Conclude the type of transformation. Since the graph of f(x) is shifted 1 unit to the left to obtain the graph of g(x), the transformation is a translation 1 unit left.

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What kind of transformation converts the graph of $f(x) = 8|x + 8| + 5$ into the graph of $g(x) = 8|x + 7| + 5$ ? $\newline$ Choices: $\newline$ (A) translation $1$ unit left $\newline$ (B) translation $1$ unit up $\newline$ (C) translation $1$ unit down $\newline$ (D) translation $1$ unit right

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Algebra 1

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = 8|x + 8| + 5

into the graph of

g(x) = 8|x + 7| + 5

\newline

Choices:

\newline

(A) translation

1

unit left

\newline

(B) translation

1

unit up

\newline

1

unit down

\newline

(D) translation

1

unit right

Analyze Functions: Analyze the given functions. $\newline$ We have $f(x) = 8|x + 8| + 5$ and $g(x) = 8|x + 7| + 5$ . We need to determine how the graph of $f(x)$ is transformed to get the graph of $g(x)$ .
Compare Absolute Value: Compare the inside of the absolute value. $\newline$ The only difference between $f(x)$ and $g(x)$ is the expression inside the absolute value. For $f(x)$ , it is $|x + 8|$ , and for $g(x)$ , it is $|x + 7|$ .
Determine Horizontal Shift: Determine the horizontal shift. $\newline$ The expression inside the absolute value for $g(x)$ is $x + 7$ , which is $x + 8 - 1$ . This indicates a horizontal shift of $1$ unit to the left.
Verify Vertical Shift: Verify that there is no vertical shift. The $+ 5$ outside the absolute value in both $f(x)$ and $g(x)$ remains unchanged, which means there is no vertical shift.
Conclude Transformation: Conclude the type of transformation. $\newline$ Since the graph of $f(x)$ is shifted $1$ unit to the left to obtain the graph of $g(x)$ , the transformation is a translation $1$ unit left.