562 Final Exam
- When we say that a real number u is the natural logarithm of some other real number
v, and that e is Euler’s constant (an irrational number equal to about 2.71828), we are
in effect saying that
(a)v equals e to the uth power.
(b)u equals e to the vth power.
(c)v equals u to the eth power.
(d)u equals v to the eth power.
(e)v to the uth power equals e. - A three-by-three linear system is consistent and not redundant if and only if
(a) it has a single, unique solution.
(b) it has two distinct solutions.
(c) it has three distinct solutions.
(d) it has infinitely many solutions.
(e) it has no solutions. - Under what circumstances can we divide both sides of an equation by the same
variable and get another valid equation?
(a) Never.
(b) Only if the variable can never become equal to 0.
(c) Only if the variable can never become negative.
(d) Only if the variable can never become irrational.
(e) Always. - The relation graphed in Fig. FE-6 is not a function of x if we think of it as a mapping
from values of x to values of y. We can see this because
(a) the curve is not a straight line.
(b) the domain is not the entire set of real numbers.
(c) the relation is not one-to-one.
(d) there are values of x that map into more than one value of y.
(e) there no values of y that map into more than one value of x. - How can we restrict the range of the relation graphed in Fig. FE-6 so that it becomes a
function of x if we think of it as a mapping from values of x to values of y?
(a) We can restrict the range to the set of non-negative reals.
(b) We can restrict the range to the set of negative reals.
(c) We can restrict the range to the set of reals larger than 1.
(d) We can restrict the range to the set of reals smaller than −1.
(e) Any of the above. - The relation graphed in Fig. FE-6 is a function of y if we think of it as a mapping
from values of y to values of x. We can see this because
(a) there are values of x that map into more than one value of y.
(b) there no values of y that map into more than one value of x.