Questions and Answers on Functions

A set of questions on the concepts of a function, in calculus, are presented along with their solutions. These questions have been designed to help you gain deep understanding of the concept of a function as well as its domain and range which are of major importance in mathematics. If you have difficulties answering a question, review the definition(s) and theorem(s) related to the question.

Question 1:

True or False. The two functions f and g defined by

f(x) = 3x + 3 for x real and g(t) = 3t + 3 for t real and positive

are equal?

Answer :

False. Two functions are equal if their rules are equal and their domains are the same.

Question 2:

If functions f and g have domains Df and Dg respectively, then the domain of f / g is given by

(A) the union of Df and Dg
(B) the intersection of Df and Dg
(C) the intersection of Df and Dg without the zeros of function g
(D) None of the above

Answer :

(C). Division by zero is not allowed in mathematics. Students tend to forget this point.

Question 3:

True or False. The graph of f(x) and that of f(x + 2) are the same

Answer :

False. The graph of f(x + 2) is that of f(x) shifted 2 units to the left.

Question 4:

Let the closed interval [a , b] be the domain of function f. The domain of f(x - 3) is given by

(A) the open interval (a , b)
(B) the closed interval [a , b]
(C) the closed interval [a - 3 , b - 3]
(D) the closed interval [a + 3 , b + 3]

Answer :

(D). The graph of f(x - 3) is that of f(x) shifted 3 units to the right. To shift the closed interval [a , b] to the right you need to add 3 units to the endpoints a and b of the interval.

Question 5:

Let the interval (a , +infinity) be the range of function f. The range of f(x) - 4 is given by

(A) the interval (a - 4 , +infinity)
(B) the interval (a + 4, +infinity)
(C) the interval (a, +infinity)
(C) None of the above

Answer :

(A). If the range of f is given by the interval (a , +infinity), we can write the following inequality

f(x) > a

add - 4 to both sides on the inequality to obtain

f(x) - 4 > a - 4

The last inequality suggests that the range of f(x) - 4 is (a - 4, +infinity)

Question 6:

True or False. The equation y = | x | , with y >= 0, represents y as a function of x.

Answer :


Question 7:

True or False. The equation x = | y | , with x >= 0, represents y as a function of x.

Answer :

False. Solve for y to find that y = | x | or y = -| x |; for one value of the independent variable x we have two values of the dependent variable y.

More references on calculus questions with answers, tutorials and problems and Questions on Functions with Solutions.

  • Linear ProgrammingNew !
  • Online Step by Step Calculus Calculators and SolversNew ! Factor Quadratic Expressions - Step by Step CalculatorNew ! Step by Step Calculator to Find Domain of a Function New !
    Free Trigonometry Questions with Answers -- Interactive HTML5 Math Web Apps for Mobile LearningNew ! -- Free Online Graph Plotter for All Devices
    Home Page -- HTML5 Math Applets for Mobile Learning -- Math Formulas for Mobile Learning -- Algebra Questions -- Math Worksheets -- Free Compass Math tests Practice
    Free Practice for SAT, ACT Math tests -- GRE practice -- GMAT practice Precalculus Tutorials -- Precalculus Questions and Problems -- Precalculus Applets -- Equations, Systems and Inequalities -- Online Calculators -- Graphing -- Trigonometry -- Trigonometry Worsheets -- Geometry Tutorials -- Geometry Calculators -- Geometry Worksheets -- Calculus Tutorials -- Calculus Questions -- Calculus Worksheets -- Applied Math -- Antennas -- Math Software -- Elementary Statistics High School Math -- Middle School Math -- Primary Math
    Math Videos From Analyzemath
    Author - e-mail

    Updated: February 2015

    Copyright 2003 - 2015 - All rights reserved