Using horizontal line test (Fig.1.35(a), 1.35(b), 1.35(c)), determine which of the following functions are one – one.

Let A = {1,2,3}, B = {4, 5, 6,7}, and f = {(1, 4),(2, 5),(3, 6)}  be a function from A to B. Show that f is one – one but not onto function.

Let f be a function from R to R defined by f(x) = 3x - 5. Find the values of a and b given that (a,4) and (1,b) belong to f.

Determine whether the graph given below represent functions. Give a reason for your answer concerning the graph.

Let A = {1, 2, 3, 4} and B = N. Let f: A ⟶ B be defined by f(x) = x³ then
(i) find the range of f
(ii) identify the type of function

In each of the following cases state whether the function is bijective or not. Justify your answer.
i. f : R ⟶ R defined by f(x) = 2x + 1
ii. f : R ⟶ R defined by f(x) = 3 - 4x²

Let A = {-1, 1} and B = {0, 2}. If the function f : A ⟶ B defined by f(x) = ax + b is an onto function? Find a and b.

The distance S an object travels under the influence of gravity in time t seconds is given by S(t) = \(\frac{1}{2}\)gt² + at + b where, (g is the acceleration due to gravity), a, b are constants. Verify whether the function S(t)  is one-one or not.

The Cartesian product A x A has 9 elements among which (–1, 0) and (0, 1) are found. Find the set A and the remaining elements of A x A.

Write the domain of the following real functions
 f(x) = \(\frac { 2x+1 }{ x-9 } \)