Question 1:
True or False. The domain of a function is the set of all real values for which the function is real valued.
Answer :
True.
Question 2:
True or False. The sign of the first derivative of a given function f informs you on the interval(s) where f(x) is positive, negative or equal to zero.
Answer :
False.
The sign of the first derivative informs you on the interval(s) where f is increasing, decreasing or constant.
Question 3:
True or False. The sign of the second derivative of a given function f informs you on the concavity of the graph of f.
Answer :
True.
Question 4:
True or False. The horizontal asymptote to the graph of a given function f is determined by finding the limit, if it exists, of f(x) as x approaches 0.
Answer :
False.
A horizontal asymptote may be determined by finding the limit of f(x) as x approches + or - infinity (very large or very small values).
Question 5:
True or False. Any value of x that makes the denominator of rational function f equal to zero, represents a vertical asymptote to the graph of f.
Answer :
False.
Not always. Let f(x) = (x + 3) / (x 2 -9).
Factor the denominator and simplify to obtain f(x) = 1 / (x - 3)
Although x = - 3 makes the denominator equal to 0 there is no vertical asymptote at x = - 3; in fact there is a hole.
Question 6:
True or False. A horizontal asymptote may intersect the graph of the function.
Answer :
True.
Example: f(x) = sin x / x
Question 7:
True or False. The x intercepts of the graph of a function corresponds to the zeros of the function.
Answer :
True.
Question 8:
True or False. A graph cannot cut its vertical asymptote.
Answer :
True.
More references on calculus
questions with answers and tutorials and problems .