The graph of f, of, x, equals, minus, 2, vertical bar, x, vertical barf(x)=−2∣x∣ is given below. Write the equation of a function g, of, xg(x) which would shift the graph of f, of, xf(x) down 3 units.

Answer 1

To shift the graph of the function \( f(x) = -2|x| \) down by 3 units, you can subtract 3 from the function \( f(x) \).

The equation of the new function \( g(x) \) can be written as:

\[ g(x) = f(x) - 3 \]

This gives us:

\[ g(x) = -2|x| - 3 \]

So the equation of \( g(x) \) is:

\[ g(x) = -2|x| - 3 \]

This function represents the graph of \( f(x) \) shifted down 3 units.