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) left 6 units.

Answer 1

To shift the graph of the function \( f(x) = 2x^2 \) left by 6 units, you can modify the input to the function. Specifically, to shift the graph to the left by \( h \) units, you replace \( x \) with \( (x + h) \).

In this case, since you want to shift left by 6 units, you will replace \( x \) with \( (x + 6) \):

\[ g(x) = f(x + 6) = 2(x + 6)^2 \]

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

\[ g(x) = 2(x + 6)^2 \]