Relations and Functions quiz

If (a, 3) = (2, b), then:

If n

The value of [-0.5] is:

The signum function at x = -5 has the value:

The domain of f(x) = sqrt(x) as a real function is:

The range of the constant function f(x) = 4 is:

The domain of f(x) = 1/x is:

The number of relations from a set of 2 elements to a set of 2 elements is:

The value of mod(-3) is:

The range of f(x) = x^2 + 2 for real x is:

Define an ordered pair and the Cartesian product of two sets. (2 marks)

If A = {a, b} and B = {1}, write B x A. (2 marks)

If f(x) = x^2, find f(-3) and (f(1.1) - f(1))/(1.1 - 1). (2 marks)

Write the domain and range of the identity function on R. (2 marks)

Find the range of f(x) = 3 - 2x for x in {-1, 0, 1, 2}. (2 marks)

If f(x) = 2x - 5 and g(x) = x^2, find (f - g)(2). (2 marks)

Define a polynomial function and a rational function with examples. (2 marks)

Find the domain of f(x) = sqrt(x - 2). (2 marks)

Explain why the relation {(1, 2), (1, 3), (2, 4)} is not a function. (2 marks)

If f(x) = x^2 - 3x + 2, find f(f(0)). (2 marks)

If P = {a, b, c} and Q = {r}, find P x Q and Q x P. Are they equal? (3 marks)

Find the domain of f(x) = (x^2 + 1)/(x^2 - 9). (3 marks)

A function is f(x) = 2x + 1 with domain {0, 1, 2, 3}. Write it as a set of ordered pairs and find its range. (3 marks)

If f(x) = x^3 - 1/x^3, show that f(x) + f(1/x) = 0. (3 marks)

Find the range of f(x) = 1 - mod(x - 2). (3 marks)

Read the passage and answer the questions. A taxi charges Rs 50 as a fixed fee plus Rs 12 per km travelled. (i) Write the fare f(x) for x km as a function. (ii) Find f(10). (iii) State a suitable domain for f. (5 marks)

Read the passage and answer the questions. The temperature in Fahrenheit is F = (9/5)C + 32, where C is the temperature in Celsius. (i) Find F when C = 0. (ii) Find F when C = -10. (iii) Find C when F = 212. (5 marks)

Read the passage and answer the questions. On the set A = {1, 2, 3, 4, 5, 6}, a relation R is defined by R = {(a, b) : b = a + 1}. (i) Write R in roster form. (ii) Write its domain and range. (iii) Is R a function from A to A? Give a reason. (5 marks)

Read the passage and answer the questions. A parking lot charges Rs 20 for every hour or part of an hour, using the rule C(t) = 20 x ([t] + 1) for 0 < t < 5, where t is not a whole number. (i) Find C(1.5). (ii) Find C(3.2). (iii) Name the special function used. (5 marks)

Read the passage and answer the questions. The area of a square depends on its side s. (i) Write the area A(s) as a function. (ii) Write a suitable domain. (iii) Find A(2.5). (5 marks)

Define a relation and a function. Explain with arrow diagrams why every function is a relation but not every relation is a function. (6 marks)

Explain the modulus, signum and greatest integer functions with their definitions, graphs, domains and ranges. (6 marks)

Explain the algebra of real functions with f(x) = x^2 and g(x) = 2x + 1, finding f + g, f - g, fg and f/g with their domains. (6 marks)

If A = {1, 2, 3, 4} and B = {5, 6}, find A x B and B x A. Show that n(A x B) = n(B x A) but A x B is not equal to B x A. (6 marks)

Find the domain and range of f(x) = sqrt(x - 1) and g(x) = 1/(x^2 + 1), and draw rough graphs of both. (6 marks)