The graph of f(x) = 2x ^ 2 is given below. Write the equation of a function g(x) which would shift the graph of f(x) down 5 units.

Answer 1

To shift the graph of the function \( f(x) = 2x^2 \) down by 5 units, you need to subtract 5 from the original function.

Thus, the equation of the new function \( g(x) \) would be:

\[ g(x) = f(x) - 5 \]

Substituting \( f(x) \) with \( 2x^2 \):

\[ g(x) = 2x^2 - 5 \]

Therefore, the equation of the function \( g(x) \) that shifts the graph of \( f(x) \) down 5 units is:

\[ g(x) = 2x^2 - 5 \]