RELATIONS AND FUNCTIONS WORKSHEET

(1)  Let f = {(x, y) | x, y ∈ N and y = 2x} be a relation on ℕ. Find the domain, co-domain and range. Is this relation a function?           Solution

(2)  Let X = {3, 4, 6, 8}. Determine whether the relation ℝ  = {(x, f (x)) | x ∈ X, f (x) = x² + 1} is a function from X to ℕ ?         Solution

(3)  Given the function f : x -> x² −5x + 6 , evaluate

(i) f (-1)

(ii) f (2a)

(iii) f (2)

(iv) f (x −1)         Solution

(4)  A graph representing the function f (x) is given figure

it is clear that f (9) = 2.

(i) Find the following values of the function

(a) f (0) (b) f (7) (c) f (2) (d) f (10)

(ii) For what value of x is f (x) = 1?

(iii) Describe the following (i) Domain (ii) Range.

(iv) What is the image of 6 under f ?          Solution

Let f (x) = 2x + 5. If x ≠ 0 then find [f(x + 2) - f(2)] / x

Solution

(5)  A function f is defined by f (x) = 2x – 3

(i) find [f(0) +  f(1)]/2

(ii) find x such that f (x) = 0.

(iii) find x such that f (x) = x .

(iv) find x such that f (x) = f (1−x) .       Solution

(6)  An open box is to be made from a square piece of material, 24 cm on a side, by cutting equal squares from the corners and turning up the sides as shown. Express the volume V of the box as a function of x.

Solution

(7)  A function f is defined by f (x) = 3−2x . Find x such that f (x²) = (f (x))²       Solution

(8)  A plane is flying at a speed of 500 km per hour. Express the distance d travelled by the plane as function of time t in hours.          Solution

(9)  The data in the adjacent table depicts the length of a woman’s forehand and her corresponding height. Based on this data, a student finds a relationship between the height (y) and the forehand length(x) as y = ax +b , where a, b are constants.

(i) Check if this relation is a function.

(ii) Find a and b.

(iii) Find the height of a woman whose forehand length is 40 cm.

(iv) Find the length of forehand of a woman if her height is 53.3 inches.        Solution

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