Question

The graph shows g(x), which is a transformation of f(x)=|x|. Write the function rule for g(x). Write your answer in the form a|x–h|+k, where a, h, and k are integers or simplified fractions. it got fliped over the x axsis
g(x)=

Answer 1

To write the function rule for \( g(x) \) as a transformation of \( f(x) = |x| \), we need to consider the effects of the transformations mentioned:

1. **Flipping over the x-axis**: This transformation changes the function from \( f(x) \) to \( -f(x) \). For the absolute value function, this means:
\[
g(x) = -|x|
\]

2. If there are horizontal or vertical shifts involved, we will incorporate those as well. The general form you mentioned is \( g(x) = a|x - h| + k \), where:
- \( a \) reflects vertical stretching or flipping,
- \( h \) represents a horizontal shift,
- \( k \) represents a vertical shift.

From your description, if \( g(x) \) is just the reflection of \( f(x) \) over the x-axis and without any shifts, then the function can be written simply as:
\[
g(x) = -|x|
\]
Here, \( a = -1 \), \( h = 0 \), and \( k = 0 \).

So, the final answer is:
\[
g(x) = -1|x - 0| + 0
\]
In simplified form, this is:
\[
g(x) = -|x|
\]