Question

Function g can be thought of as a

translated (shifted) version of
f(x) = x².
-7-6-5-4-3-2
it
2
655424
23
B
5
-6
7
Y
4
2 3 4 5 6 7
X

Answer 1

The equation for g(x) is; g(x) = (x + 2)² + 1

The the steps used to obtain the above equation for g(x) can be presented as follows;

Please find attached the possible graph of the functions f and function g created using MS Excel, obtained from a similar question found through search, we get;

The coordinate point of the vertex of the function f = (0, 0)

The coordinate point of the corresponding vertex of the function g = (-2, 1)

Therefore, the function g appeared to be shifted one unit upwards and two units to the left, which can be expressed as follows;

The rule for the vertical translation of the function f is f + a

The rule for the horizontal translation of the function f is f(x + b), where the variable b is positive for a shift to the left and negative for a shift to the right, therefore;

The function g is therefore; f(x + 2) + 1

g(x) = (x + 2)² + 1