Читать книгу Calculus Equations And Answers (Speedy Study Guides) - Speedy Publishing - Страница 3

CALCULUS EQUATIONS AND ANSWERS

Functions

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]