Question

Given the function f(x)=x^2 and k=2, which of the following represents a horizontal shift?
F(x)+k, kf(x), f(x+k), f(kx)

Answer 1

f(x) = x²
k = 2

f(x) + k = x² + 2
    
    kf(x) = 2x²

f(x + k) = (x + 2)²
f(x + k) = (x + 2)(x + 2)
f(x + k) = x(x + 2) + 2(x + 2)
f(x + k) = x(x) + x(2) + 2(x) + 2(2)
f(x + k) = x² + 2x + 2x + 4
f(x + k) = x² + 4x + 4

f(kx) = (2x)²
f(kx) = 4x²

The answers are f(x) + k and f(x + k).