What kind of transformation converts the graph of f(x) = 2|x - 3| + 7 into the graph of g(x) = 2|x + 7| + 7? Choices: (A)translation 10 units left (B)translation 10 units down (C)translation 10 units right (D)translation 10 units up

Identify Vertex f(x): Identify the vertex of the function f(x) = 2|x - 3| + 7. The vertex is at (3, 7) because the absolute value function has its vertex where the expression inside the absolute value is zero.Identify Vertex g(x): Identify the vertex of the function g(x) = 2|x + 7| + 7. The vertex is at (-7, 7) because the absolute value function has its vertex where the expression inside the absolute value is zero.Determine Horizontal Shift: Determine the horizontal shift between the vertices of f(x) and g(x). The shift is from (3, 7) to (-7, 7), which is 10 units to the left.Match Transformation: Match the transformation with the given choices. The transformation is a translation 10 units left, which corresponds to choice (A).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What kind of transformation converts the graph of $f(x) = 2|x - 3| + 7$ into the graph of $g(x) = 2|x + 7| + 7$ ? $\newline$ Choices: $\newline$ (A) translation $10$ units left $\newline$ (B) translation $10$ units down $\newline$ (C) translation $10$ units right $\newline$ (D) translation $10$ units up

View step-by-step help

Home

Math Problems

Algebra 2

Describe function transformations

Full solution

Q. What kind of transformation converts the graph of

f(x) = 2|x - 3| + 7

into the graph of

g(x) = 2|x + 7| + 7

\newline

Choices:

\newline

(A) translation

10

units left

\newline

(B) translation

10

units down

\newline

10

units right

\newline

(D) translation

10

units up

Identify Vertex $f(x)$ : Identify the vertex of the function $f(x) = 2|x - 3| + 7$ . The vertex is at $(3, 7)$ because the absolute value function has its vertex where the expression inside the absolute value is zero.
Identify Vertex $g(x)$ : Identify the vertex of the function $g(x) = 2|x + 7| + 7$ . The vertex is at $(-7, 7)$ because the absolute value function has its vertex where the expression inside the absolute value is zero.
Determine Horizontal Shift: Determine the horizontal shift between the vertices of $f(x)$ and $g(x)$ . The shift is from $(3, 7)$ to $(-7, 7)$ , which is $10$ units to the left.
Match Transformation: Match the transformation with the given choices. $\newline$ The transformation is a translation $10$ units left, which corresponds to choice $(A)$ .