Answer:
g(x) = (x + 1)^2 + 3
Step-by-step explanation:
When x is replaced by x - h, it results in a horizontal translation of h units.
When y is replaced by y - k, it results in a vertical translation of k units.
f(x) = x^2 is the original function.
Rewrite it as
y = x^2
To translate it 1 unit left, you need h = -1.
x - h = x - (-1) = x + 1. Replace x with x + 1.
Now you have y = (x + 1)^2.
To translate 3 units up, you have k = 3.
y - k = y - 3. Replace y with y - 3.
y - 3 = (x + 1)^2
Solve for y.
y = (x + 1)^2 + 3
Replace y with g(x).
g(x) = (x + 1)^2 + 3
