What kind of transformation converts the graph of f(x) = -9|x + 6| + 2 into the graph of g(x) = -9|x + 6| - 8? Choices: (A)translation 10 units down (B)translation 10 units left (C)translation 10 units up (D)translation 10 units right

Analyze Functions: Analyze the given functions. We have f(x) = -9|x + 6| + 2 and g(x) = -9|x + 6| - 8. Notice that the only difference between f(x) and g(x) is the constant term at the end of the function.Type of Transformation: Determine the type of transformation. Since the only change is in the constant term, and the change is from +2 to -8, this indicates a vertical shift.Calculate Vertical Shift: Calculate the amount of vertical shift. The change in the constant term is from +2 to -8, which is a decrease of 10 units. To find the amount of shift: -8 - (+2) = -10. This means the graph has shifted 10 units down.Match with Choices: Match the transformation with the given choices. The graph has shifted 10 units down, so the correct choice is (A) translation 10 units down.

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 $f(x) = -9|x + 6| + 2$ into the graph of $g(x) = -9|x + 6| - 8$ ? $\newline$ Choices: $\newline$ (A) translation $10$ units down $\newline$ (B) translation $10$ units left $\newline$ (C) translation $10$ units up $\newline$ (D) translation $10$ units right

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| + 2

into the graph of

g(x) = -9|x + 6| - 8

\newline

Choices:

\newline

(A) translation

10

units down

\newline

(B) translation

10

units left

\newline

10

units up

\newline

(D) translation

10

units right

Analyze Functions: Analyze the given functions. $\newline$ We have $f(x) = -9|x + 6| + 2$ and $g(x) = -9|x + 6| - 8$ . $\newline$ Notice that the only difference between $f(x)$ and $g(x)$ is the constant term at the end of the function.
Type of Transformation: Determine the type of transformation. $\newline$ Since the only change is in the constant term, and the change is from $+2$ to $-8$ , this indicates a vertical shift.
Calculate Vertical Shift: Calculate the amount of vertical shift. $\newline$ The change in the constant term is from $+2$ to $-8$ , which is a decrease of $10$ units. $\newline$ To find the amount of shift: $-8 - (+2) = -10$ . $\newline$ This means the graph has shifted $10$ units down.
Match with Choices: Match the transformation with the given choices. $\newline$ The graph has shifted $10$ units down, so the correct choice is (A) translation $10$ units down.