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) right 1 unit.

Answer 1

To shift the graph of the function \( f(x) = 2x^2 \) to the right by 1 unit, you can use the transformation rule for horizontal shifts. Shifting a function to the right by \( h \) units involves replacing \( x \) with \( (x - h) \).

In this case, since you want to shift right by 1 unit, you will replace \( x \) with \( (x - 1) \). Thus, the new function \( g(x) \) will be:

\[ g(x) = f(x - 1) = 2(x - 1)^2 \]

So the equation of the function \( g(x) \) that represents the graph of \( f(x) = 2x^2 \) shifted right by 1 unit is:

\[ g(x) = 2(x - 1)^2 \]