What kind of transformation converts the graph of f(x) = (x + 7)^2 + 3 into the graph of g(x) = (x + 7)^2 + 1? Choices: (A)translation 2 units up (B)translation 2 units left (C)translation 2 units down (D)translation 2 units right

Analyze Functions: Analyze the given functions. We have f(x) = (x + 7)^2 + 3 and g(x) = (x + 7)^2 + 1. Compare the two functions to determine the type of transformation.Identify Change: 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 +3, and g(x) has +1.Determine Transformation: Determine the direction of the transformation. Since the change is in the constant term, and it is decreasing from +3 to +1, the transformation is vertical.Calculate Magnitude: Calculate the magnitude of the transformation. The change in the constant term is from +3 to +1, which is a decrease of 2 units.Conclude Transformation: Conclude the type of transformation. The graph of f(x) is moving down by 2 units to become g(x). This is a translation 2 units down.

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What kind of transformation converts the graph of $f(x) = (x + 7)^2 + 3$ into the graph of $g(x) = (x + 7)^2 + 1$ ? $\newline$ Choices: $\newline$ (A) translation $2$ units up $\newline$ (B) translation $2$ units left $\newline$ (C) translation $2$ units down $\newline$ (D) translation $2$ 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) = (x + 7)^2 + 3

into the graph of

g(x) = (x + 7)^2 + 1

\newline

Choices:

\newline

(A) translation

2

units up

\newline

(B) translation

2

units left

\newline

2

units down

\newline

(D) translation

2

units right

Analyze Functions: Analyze the given functions. $\newline$ We have $f(x) = (x + 7)^2 + 3$ and $g(x) = (x + 7)^2 + 1$ . Compare the two functions to determine the type of transformation.
Identify Change: 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. $f(x)$ has $+3$ , and $g(x)$ has $+1$ .
Determine Transformation: Determine the direction of the transformation. $\newline$ Since the change is in the constant term, and it is decreasing from $+3$ to $+1$ , the transformation is vertical.
Calculate Magnitude: Calculate the magnitude of the transformation. $\newline$ The change in the constant term is from $+3$ to $+1$ , which is a decrease of $2$ units.
Conclude Transformation: Conclude the type of transformation. $\newline$ The graph of $f(x)$ is moving down by $2$ units to become $g(x)$ . This is a translation $2$ units down.