Write a linear function F with F (0) = 2 and F (2) = 4

f (x) = x + 2

Step-by-step explanation:

A linear function has the form

f (x) = mx + c

Evaluate f (0) = 2, that is

2 = m (0) + c

2 = 0 + c ⇒ c = 2

Evaluate f (2) = 4, that is

4 = 2m + c ← substitute c = 2

4 = 2m + 2 (subtract 2 from both sides)

2 = 2m (divide both sides by 2)

1 = m

Hence

f (x) = x + 2 ← is a possible linear function