What kind of transformation converts the graph of f(x) = 9|x + 8| + 3 into the graph of g(x) = 9|x + 8| + 7? Choices: (A)translation 4 units right (B)translation 4 units down (C)translation 4 units left (D)translation 4 units up

Identify Structure: Identify the structure of the given functions. Compare f(x) = 9|x + 8| + 3 and g(x) = 9|x + 8| + 7 to see the difference.Determine Transformation Type: Determine the type of transformation. The only difference between f(x) and g(x) is the constant term at the end of the equation. This indicates a vertical shift.Calculate Vertical Shift: Calculate the amount and direction of the vertical shift. The constant term in f(x) is +3, and in g(x) it is +7. To go from +3 to +7, we add 4.Conclude Transformation Type: Conclude the type of transformation. Since we are adding 4 to the constant term to get from f(x) to g(x), the graph of f(x) is shifted 4 units up to become the graph of g(x).

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What kind of transformation converts the graph of $f(x) = 9|x + 8| + 3$ into the graph of $g(x) = 9|x + 8| + 7$ ? $\newline$ Choices: $\newline$ (A) translation $4$ units right $\newline$ (B) translation $4$ units down $\newline$ (C) translation $4$ units left $\newline$ (D) translation $4$ units up

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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 + 8| + 3

into the graph of

g(x) = 9|x + 8| + 7

\newline

Choices:

\newline

(A) translation

4

units right

\newline

(B) translation

4

units down

\newline

4

units left

\newline

(D) translation

4

units up

Identify Structure: Identify the structure of the given functions. Compare $f(x) = 9|x + 8| + 3$ and $g(x) = 9|x + 8| + 7$ to see the difference.
Determine Transformation Type: Determine the type of transformation. $\newline$ The only difference between $f(x)$ and $g(x)$ is the constant term at the end of the equation. This indicates a vertical shift.
Calculate Vertical Shift: Calculate the amount and direction of the vertical shift. $\newline$ The constant term in $f(x)$ is $+3$ , and in $g(x)$ it is $+7$ . To go from $+3$ to $+7$ , we add $4$ .
Conclude Transformation Type: Conclude the type of transformation. $\newline$ Since we are adding $4$ to the constant term to get from $f(x)$ to $g(x)$ , the graph of $f(x)$ is shifted $4$ units up to become the graph of $g(x)$ .