What kind of transformation converts the graph of f(x) = -10|x + 6| - 6 into the graph of g(x) = -10|x + 5| - 6? Choices: (A)translation 1 unit right (B)translation 1 unit up (C)translation 1 unit left (D)translation 1 unit down

Identify Vertex: Identify the vertex of the absolute value function f(x). The vertex of f(x) = -10|x + 6| - 6 is at the point where the expression inside the absolute value is zero, which is at x = -6. The vertex is (-6, -6).Identify Vertex: Identify the vertex of the absolute value function g(x). The vertex of g(x) = -10|x + 5| - 6 is at the point where the expression inside the absolute value is zero, which is at x = -5. The vertex is (-5, -6).Compare Vertices: Compare the vertices of f(x) and g(x) to determine the transformation. The vertex of f(x) is at (-6, -6) and the vertex of g(x) is at (-5, -6). The y-coordinates are the same, so there is no vertical shift. The x-coordinate of g(x) is 1 unit greater than the x-coordinate of f(x), indicating a horizontal shift to the right.Determine Shift: Determine the direction and magnitude of the horizontal shift. Since the x-coordinate of the vertex of g(x) is 1 unit greater than the x-coordinate of the vertex of f(x), the graph of f(x) has been translated 1 unit to the right to obtain the graph of g(x).

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What kind of transformation converts the graph of $f(x) = -10|x + 6| - 6$ into the graph of $g(x) = -10|x + 5| - 6$ ? $\newline$ Choices: $\newline$ (A) translation $1$ unit right $\newline$ (B) translation $1$ unit up $\newline$ (C) translation $1$ unit left $\newline$ (D) translation $1$ unit down

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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) = -10|x + 6| - 6

into the graph of

g(x) = -10|x + 5| - 6

\newline

Choices:

\newline

(A) translation

1

unit right

\newline

(B) translation

1

unit up

\newline

1

unit left

\newline

(D) translation

1

unit down

Identify Vertex: Identify the vertex of the absolute value function $f(x)$ . The vertex of $f(x) = -10|x + 6| - 6$ is at the point where the expression inside the absolute value is zero, which is at $x = -6$ . The vertex is $(-6, -6)$ .
Identify Vertex: Identify the vertex of the absolute value function $g(x)$ . The vertex of $g(x) = -10|x + 5| - 6$ is at the point where the expression inside the absolute value is zero, which is at $x = -5$ . The vertex is $(-5, -6)$ .
Compare Vertices: Compare the vertices of $f(x)$ and $g(x)$ to determine the transformation. $\newline$ The vertex of $f(x)$ is at $(-6, -6)$ and the vertex of $g(x)$ is at $(-5, -6)$ . The $y$ -coordinates are the same, so there is no vertical shift. The $x$ -coordinate of $g(x)$ is $1$ unit greater than the $x$ -coordinate of $f(x)$ , indicating a horizontal shift to the right.
Determine Shift: Determine the direction and magnitude of the horizontal shift. Since the $x$ -coordinate of the vertex of $g(x)$ is $1$ unit greater than the $x$ -coordinate of the vertex of $f(x)$ , the graph of $f(x)$ has been translated $1$ unit to the right to obtain the graph of $g(x)$ .