The graph of f(x) = - x ^ 2 is given below. Write the equation of a function g(x) which would shift the graph of f(x) right 6 units and down 4 units.

Answer 1

To shift the graph of the function \( f(x) = -x^2 \) right by 6 units, you replace \( x \) with \( (x - 6) \). This gives you:

\[ f(x - 6) = -(x - 6)^2 \]

Next, to shift the graph down by 4 units, you subtract 4 from the entire function. This results in:

\[ g(x) = -(x - 6)^2 - 4 \]

Thus, the equation of the function \( g(x) \) that shifts the graph of \( f(x) \) right 6 units and down 4 units is:

\[ g(x) = -(x - 6)^2 - 4 \]