Mathematics I (Calculus) - Old Questions

1. (a) A function is defined by ,  calculate f(-1),f(3), and sketch the  graph.(5)

Given,

Since -1<0, f(-1) = -1 + 2 = 1

Since 3>0, f(3) = 1 - 3 = -2

To draw graph, calculating the points:

For f(x) = x+2 if x<0

    f(-1) = -1+2 =1  ⇒ (-1, 1)

    f(-2) = -2+2 = 0  ⇒ (-2, 0)

    f(-3) = -3+2 = -1  ⇒ (-3, -1) and so on.

For f(x) =1-x if x>0

    f(1) = 1-1 = 0  ⇒ (1, 0)

    f(2) = 1-2 = -1  ⇒ (2, -1)

    f(3)= 1-3 = -2  ⇒ (3, -2) and so on.

Plotting these points of both functions we get;