Question

Write the rule of a function g whose graph can be obtained from the graph of the function f(x) = x^2 - x + 3 by reflecting the graph in the x-axis, then shifting it vertically downward 4 units.

Answer 1

If you reflect a graph on the x-axis, positive f(x) becomes negative f(x)
shifting down f(x) --> f(x) - 4

so

\[g(x) = -f(x)-4 = -x^2+x-3-4= -x^2+x-7\]

Answer 2

Thank you!