The graph of f(x) = x ^ 2 is given below. Write the equation of a function g(x) which would shift the graph of f(x) left 1 unit and down 4 units.

Answer 1

To shift the graph of the function \( f(x) = x^2 \) left by 1 unit, you replace \( x \) with \( (x + 1) \). To shift the graph down by 4 units, you subtract 4 from the entire function.

Starting with \( f(x) = x^2 \):

1. Shift left by 1 unit: \( f(x + 1) = (x + 1)^2 \)
2. Shift down by 4 units: \( g(x) = (x + 1)^2 - 4 \)

The final equation of the function \( g(x) \) is: \[ g(x) = (x + 1)^2 - 4 \]