s
Section 5.4 Functions
403
2. The accompanying figure illustrates various binary relations from R to R. Which are functions? For those
that are functions, which are onto? Which are one-to-one?
(a)
(b)
(c)
(d)
3. Using the equation f (x) = 2x − 1 to describe the functional association, write the function as a set of
ordered pairs if the codomain is R and the domain is
a. S = 50, 1, 26.
b. S = 51, 2, 4, 56.
c. S = 5"7, 1.56.
4. Using the equation f (x) = x
2
+ 1 to describe the functional association, write the function as a set of
ordered pairs if the codomain is Z and the domain is
a. S = 51, 56.
b. S = 5−1, 2, −26.
c. S = 5−"12, 36.
5. If f : Z S Z is defined by f (x) = 3x, find f (A) for
a. A = 51, 3, 56.
b. A = 5x 0 x [ Z and ( E y)(y [ Z and x = 2y)6.
6. If f : R S R is defined by f (x) = x
2
, describe
a. f (N).
b. f (Z).
c. f (R).
Section 5.4 Functions
403
2. The accompanying figure illustrates various binary relations from R to R. Which are functions? For those
that are functions, which are onto? Which are one-to-one?
(a)
(b)
(c)
(d)
3. Using the equation f (x) = 2x − 1 to describe the functional association, write the function as a set of
ordered pairs if the codomain is R and the domain is
a. S = 50, 1, 26.
b. S = 51, 2, 4, 56.
c. S = 5"7, 1.56.
4. Using the equation f (x) = x
2
+ 1 to describe the functional association, write the function as a set of
ordered pairs if the codomain is Z and the domain is
a. S = 51, 56.
b. S = 5−1, 2, −26.
c. S = 5−"12, 36.
5. If f : Z S Z is defined by f (x) = 3x, find f (A) for
a. A = 51, 3, 56.
b. A = 5x 0 x [ Z and ( E y)(y [ Z and x = 2y)6.
6. If f : R S R is defined by f (x) = x
2
, describe
a. f (N).
b. f (Z).
c. f (R).