Question

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