Let g(x) be the reflection of f(x) = x squared+ 3 in the x-axis. What is a function rule for g(x)?

1 Answer

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embizze | High School Teacher | (Level 2) Educator Emeritus

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g(x) is the reflection of `f(x)=x^2+3` in the x-axis.

To reflect over the x-axis we change all y values to -y; alternatively if `y=af(x-h)+k` , then the reflection is achieved by multiplying y by (-1).

Thus `g(x)=-x^2-3`

The graph of f(x) in red, g(x) in green: