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

Answer 1

To shift the graph of the function \( f(x) = -|x| \) to the right by 2 units, you can modify the input of the function. The general rule for shifting the graph of a function \( f(x) \) to the right by \( c \) units is to replace \( x \) with \( x - c \).

In this case, \( c = 2 \). Therefore, to shift the graph of \( f(x) \) to the right by 2 units, the new function \( g(x) \) will be:

\[ g(x) = f(x - 2) \]

Substituting \( f(x) \) into this expression, we get:

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

Thus, the equation of the function \( g(x) \) that shifts the graph of \( f(x) \) right 2 units is:

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