Question

Write an equation for the
function graphed above

Answer 1

g(x) = (x + 1)² + 1

Explanation:

the original function

f(x) = x²

for the new function g(x)

it is shifted 1 unit to the left and 1 unit up.

the shift to the left is done by adding these units to the input variable x :

g(x) = f(x+1) = (x+1)²

that way we get the function value for x+1 already at x :

1 unit "earlier" than in the original.

and the shift up is easy.

whatever the function calculates, we simply add 1 to everything.

the whole curve stays as it is, just one unit higher. g

so, the final g(x) = f(x+1) + 1 = (x + 1)² + 1