Question

Let g(x) be the reflection of f(x) = x² + 5 in the x-axis. What is a function rule for g(x)?

Answer 1

Here, f(x) = (x^2) +5. The graph of this function will be a parabola and lie on the positive y-axis. Because, both x^2 and 5 are positive and the result is positive. But, of g(x) is the reflection of f(x) mean g(x) = -f(x) = - {(x^2) +5} = - (x^2) - 5. now, the graph of g(x) will lie on the negative x-axis.