Given that: f = {(0, -5), (1, -2), (3, 4), (4, 7)} be a function from Z to Z defined by linear function.

We know that, linear functions are of the form y = mx + b

Let f(x) = ax + b, for some integers a, b

Here, (0, -5) ∈ f

⇒ f(0) = -5

⇒ a(0) + b = -5

⇒ b = -5 …(i)

Similarly, (1, -2) ∈ f

⇒ f(1) = -2

⇒ a(1) + b = -2

⇒ a + b = -2

⇒ a + (-5) = -2 [from (i)]

⇒ a = -2 + 5

⇒ a = 3

∴ f(x) = ax + b

= 3x + (-5)

f(x) = 3x - 5