Question

The graph of f, of, x, equals, minus, 2, square root of, x, end square rootf(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) up 2 units.

Answer 1

To shift the graph of the function \( f(x) = -2\sqrt{x} \) up by 2 units, you simply add 2 to the entire function.

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

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

Substituting \( f(x) \) into this equation:

\[
g(x) = -2\sqrt{x} + 2
\]

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

\[
g(x) = -2\sqrt{x} + 2
\]