What kind of transformation converts the graph of f(x) = 9|x + 1| into the graph of g(x) = 9|x + 1| - 2? Choices: (A)translation 2 units down (B)translation 2 units right (C)translation 2 units up (D)translation 2 units left

Compare Functions: To determine the type of transformation, we need to compare the functions f(x) and g(x). The function g(x) is obtained from f(x) by subtracting 2 from it. This means that every y-value of f(x) is decreased by 2 to get the corresponding y-value of g(x). This is a vertical shift.Vertical Shift Explanation: A vertical shift downwards by k units is represented by subtracting k from the function. Since g(x) = f(x) - 2, this corresponds to a vertical shift of 2 units down.Eliminate Other Options: We can rule out the other options because they involve horizontal shifts (left or right) or a vertical shift upwards, none of which are represented by subtracting 2 from the entire function.

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 $f(x) = 9|x + 1|$ into the graph of $g(x) = 9|x + 1| - 2$ ? $\newline$ Choices: $\newline$ (A) translation $2$ units down $\newline$ (B) translation $2$ units right $\newline$ (C) translation $2$ units up $\newline$ (D) translation $2$ units left

View step-by-step help

Home

Math Problems

Precalculus

Describe function transformations

Full solution

Q. What kind of transformation converts the graph of

f(x) = 9|x + 1|

into the graph of

g(x) = 9|x + 1| - 2

\newline

Choices:

\newline

(A) translation

2

units down

\newline

(B) translation

2

units right

\newline

2

units up

\newline

(D) translation

2

units left

Compare Functions: To determine the type of transformation, we need to compare the functions $f(x)$ and $g(x)$ . The function $g(x)$ is obtained from $f(x)$ by subtracting $2$ from it. This means that every $y$ -value of $f(x)$ is decreased by $2$ to get the corresponding $y$ -value of $g(x)$ . This is a vertical shift.
Vertical Shift Explanation: A vertical shift downwards by $k$ units is represented by subtracting $k$ from the function. Since $g(x) = f(x) - 2$ , this corresponds to a vertical shift of $2$ units down.
Eliminate Other Options: We can rule out the other options because they involve horizontal shifts (left or right) or a vertical shift upwards, none of which are represented by subtracting $2$ from the entire function.