Write the function rule for the function shown below reflected in the given axis.
f(x)x; -axis
Let g(x) be the reflection of f(x) in the -axis. What is the function rule for g(x)?
The function f(x) = x reflected in the -axis becomes g(x) = -x.
The function rule for g(x) can be found by reflecting f(x) in the -axis. The reflection in the -axis essentially flips the function upside down.
So if f(x) = x, then g(x) would be the function where every y-coordinate is the negative of f(x).
Thus, the function rule for g(x) would be g(x) = -x.
To find the function rule for the reflection of f(x) in the -axis, we need to understand that the reflection in the -axis flips the sign of the y-coordinate.
The given function rule for f(x) is f(x) = x.
To reflect f(x) in the -axis, we need to flip the sign of the y-coordinate. Since the y-coordinate is equal to x, we can simply change the sign of x in the function rule.
Therefore, the function rule for g(x), the reflection of f(x) in the -axis, is g(x) = -x.