What kind of transformation converts the graph of f(x) = 9|x - 6| - 4 into the graph of g(x) = 9|x - 6| - 7? Choices: (A)translation 3 units down (B)translation 3 units right (C)translation 3 units up (D)translation 3 units left

Identify Structure of Functions: Identify the basic structure of the functions f(x) and g(x). f(x) = 9|x - 6| - 4 is in the form of y = a|x - h| + k, where (h, k) is the vertex of the graph. g(x) = 9|x - 6| - 7 is also in the same form with a different k value.Compare K Values: Compare the k values of f(x) and g(x). The k value in f(x) is -4, and the k value in g(x) is -7. The change in k value is from -4 to -7, which is a decrease of 3 units.Determine Transformation Direction: Determine the direction of the transformation. Since the k value decreased by 3 units, the graph moves vertically. A decrease in k value means the graph shifts downward.Identify Transformation Type: Identify the type of transformation. The graph of f(x) has been shifted 3 units down to get the graph of g(x). This is a vertical translation.

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 $f(x) = 9|x - 6| - 4$ into the graph of $g(x) = 9|x - 6| - 7$ ? $\newline$ Choices: $\newline$ (A) translation $3$ units down $\newline$ (B) translation $3$ units right $\newline$ (C) translation $3$ units up $\newline$ (D) translation $3$ units left

View step-by-step help

Home

Math Problems

Algebra 1

Describe function transformations

Full solution

Q. What kind of transformation converts the graph of

f(x) = 9|x - 6| - 4

into the graph of

g(x) = 9|x - 6| - 7

\newline

Choices:

\newline

(A) translation

3

units down

\newline

(B) translation

3

units right

\newline

3

units up

\newline

(D) translation

3

units left

Identify Structure of Functions: Identify the basic structure of the functions $f(x)$ and $g(x)$ . $f(x) = 9|x - 6| - 4$ is in the form of $y = a|x - h| + k$ , where $(h, k)$ is the vertex of the graph. $g(x) = 9|x - 6| - 7$ is also in the same form with a different $k$ value.
Compare K Values: Compare the $k$ values of $f(x)$ and $g(x)$ . The $k$ value in $f(x)$ is $-4$ , and the $k$ value in $g(x)$ is $-7$ . The change in $k$ value is from $-4$ to $-7$ , which is a decrease of $f(x)$ $2$ units.
Determine Transformation Direction: Determine the direction of the transformation. Since the $k$ value decreased by $3$ units, the graph moves vertically. A decrease in $k$ value means the graph shifts downward.
Identify Transformation Type: Identify the type of transformation. $\newline$ The graph of $f(x)$ has been shifted $3$ units down to get the graph of $g(x)$ . $\newline$ This is a vertical translation.