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 and down 2 units.

Answer 1

To create the function \( g(x) \) from \( f(x) = 2x^2 \) that shifts the graph right 1 unit and down 2 units, we can follow these steps:

1. Shift Right 1 Unit: To shift a graph to the right by 1 unit, we replace \( x \) with \( (x - 1) \). Thus, \( f(x) \) becomes: \[ f(x - 1) = 2(x - 1)^2 \]

2. Shift Down 2 Units: To shift a graph down by 2 units, we subtract 2 from the function. Therefore, we adjust the previous equation: \[ g(x) = 2(x - 1)^2 - 2 \]

Putting it all together, the equation of the function \( g(x) \) is: \[ g(x) = 2(x - 1)^2 - 2 \]