let g(x) be the reflection of f(x)=x^2+5 in the x axis what is the function rule for g(x)
g(x)-x^2-5
g(x)x^2+5
g(x)x^2-5
g(x)-x^2+5
The correct function rule for g(x), the reflection of f(x)=x^2+5 in the x-axis, is g(x) = -x^2 - 5.
To find the reflection of a function f(x) in the x-axis, we need to change the sign of the y-coordinates.
In this case, the function f(x) is given as f(x) = x^2 + 5. So, to reflect f(x) in the x-axis, we need to change the sign of the y-coordinates, which means subtracting the function from 0.
Therefore, the function rule for g(x), the reflection of f(x) in the x-axis, is:
g(x) = -f(x) = -(x^2 + 5) = -x^2 - 5
So, the correct function rule for g(x) is: g(x) = -x^2 - 5.
To find the function rule for the reflection of f(x) = x^2 + 5 in the x-axis, we need to reflect the graph of f(x) horizontally.
To reflect a function in the x-axis, we change the sign of the function. This means that if the original function is f(x), the reflected function would be -f(x).
Applying this concept to f(x) = x^2 + 5, the reflection g(x) would be:
g(x) = -(x^2 + 5)
Simplifying the expression, we get:
g(x) = -x^2 - 5
Therefore, the function rule for g(x), the reflection of f(x) = x^2 + 5 in the x-axis, is g(x) = -x^2 - 5. Hence, the correct option is g(x) = -x^2 - 5.