What kind of transformation converts the graph of f(x) = (x - 1)^2 - 4 into the graph of g(x) = (x - 1)^2 - 3? Choices: (A)translation 1 unit up (B)translation 1 unit right (C)translation 1 unit down (D)translation 1 unit left

Analyze Functions: Analyze the given functions to determine the type of transformation. We have f(x) = (x - 1)^2 - 4 and g(x) = (x - 1)^2 - 3. The only difference between f(x) and g(x) is the constant term at the end of the equation. This indicates a vertical shift.Vertical Shift Direction: Determine the direction of the vertical shift. Since g(x) has a constant term that is 1 unit greater than the constant term in f(x), this means the graph of f(x) has been shifted up by 1 unit to become g(x).Verify Transformation: Verify the transformation by comparing the y-values of the vertices of the parabolas. The vertex of f(x) is at (1, -4) and the vertex of g(x) is at (1, -3). The y-coordinate of the vertex of g(x) is 1 unit higher than the y-coordinate of the vertex of f(x), confirming the upward shift.

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What kind of transformation converts the graph of $f(x) = (x - 1)^2 - 4$ into the graph of $g(x) = (x - 1)^2 - 3$ ? $\newline$ Choices: $\newline$ (A) translation $1$ unit up $\newline$ (B) translation $1$ unit right $\newline$ (C) translation $1$ unit down $\newline$ (D) translation $1$ unit 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) = (x - 1)^2 - 4

into the graph of

g(x) = (x - 1)^2 - 3

\newline

Choices:

\newline

(A) translation

1

unit up

\newline

(B) translation

1

unit right

\newline

1

unit down

\newline

(D) translation

1

unit left

Analyze Functions: Analyze the given functions to determine the type of transformation. We have $f(x) = (x - 1)^2 - 4$ and $g(x) = (x - 1)^2 - 3$ . The only difference between $f(x)$ and $g(x)$ is the constant term at the end of the equation. This indicates a vertical shift.
Vertical Shift Direction: Determine the direction of the vertical shift. $\newline$ Since $g(x)$ has a constant term that is $1$ unit greater than the constant term in $f(x)$ , this means the graph of $f(x)$ has been shifted up by $1$ unit to become $g(x)$ .
Verify Transformation: Verify the transformation by comparing the $y$ -values of the vertices of the parabolas. $\newline$ The vertex of $f(x)$ is at $(1, -4)$ and the vertex of $g(x)$ is at $(1, -3)$ . The $y$ -coordinate of the vertex of $g(x)$ is $1$ unit higher than the $y$ -coordinate of the vertex of $f(x)$ , confirming the upward shift.