Question

The function f(x) = 2x − 1 is transformed to function g through a horizontal shift of 7 units left. What is the equation of function g?

Answer 1

Greetings from Brasil...

If we have a translation for left/right, we have to use the expression:

F(X ± C)

if F(X + C), so the function shifted C units to the left

if F(X - C), so the function shifted C units to the right

Bringing to our problem

G(X) = F(X + C)

F(X) = 2X - 1

G(X) = F(X + 7) = 2.(X + 7) - 1

G(X) = F(X + 7) = 2X + 14 - 1

G(X) = F(X + 7) = 2X + 13

G(X) = 2X + 13