Question

Write a function g in terms of f so that the statement is true.

The graph of g is a horizontal translation 2 units right of the graph of f.
g(x)=

Answer 1

F(x+2)

The function g takes an input in the form of x returns the output in the form of f(x+2). The function g will translate the input by 2 units right of the graph of the function f.

Answer 2

To horizontally translate the graph of function f(x) 2 units to the right, the corresponding function g(x) is defined as g(x) = f(x - 2), where x is replaced with x - 2 in f.

To achieve a horizontal translation of 2 units to the right for the function f(x), you can express g(x) as g(x) = f(x - 2).

The key idea is that replacing x with x - 2 in the function f shifts the graph horizontally to the right by 2 units.

This is because, when x is decreased by 2, the function value at that point corresponds to the value of f at x = 2 units to the right.

Therefore, g(x) is effectively f translated 2 units right. The general form for a horizontal translation of c units to the right is g(x) = f(x - c).