Is f a linear transformation?

Question

Let f be defined by f(x) = -6x. Is f a linear transformation?

a. f (x+y) = ?

f (x) + f (y) = ?

Does f(x+y) = f (x) + f (y) for all x, y∈R?

b. f (cx) = ?

c (f (x)) = ?

Does f (cx) = c (f (x)) for all c x∈R?

c. Is f a linear transformation?

Answer 1

f(x + y) = -6(x + y) = -6x + -6y = f(x) + f(y)

f(cx) = -6(cx) = c(-6x) = cf(x)

So, f is a linear transformation.