L15
1. Which of the following is/are true with respect to the polynomial
()
(
)
5
234
(1 2 ) (2 ) ( 5) 3fx x x x x x=โ โ โ + โ ?
A. It is positive on the interval (3, )
+
โ. (Use the leading coefficient)
B. It behaves as 15
4
x
when xโ+โ. (Use the end behavior)
C. It touches the x-axis at 1
2
x
=
and crosses it at 0
x
=
. (Use
multiplicities of the zeros.)
2. The graph of
(
)
f
x is given. Determine
(a) if the degree of
(
)
f
x is even or
odd;
(b) if the leading coefficient is
positive or negative;
(c) what is the smallest possible
degree of
(
)
f
x.
3. Solve the inequality:
()()()
(
)
12 13 51 40
212 1 5 1 0xx xx xโโ++โฅ.
4. By solving a certain inequality, find the
interval(s) on the x-axis on which the graph
of
()
2
f
xx= lies below the graph of
(
)
2gx x
=
+. Demonstrate your answer by
graphing the functions.
5. Which of the following polynomial functions might have this graph?
(Hint: use zeros and their multiplicities and the end behavior)
(
)
(
)
(
)
(
)( )
2
2
41234fx x x x x x
=
+โ โโ
(
)
(
)
(
)
(
)( )
2
3 1234gx x x x x x
=
+โ โ โ
(
)
(
)
(
)
(
)( )
4
212 34hx x x x x x
=
โ+โ โโ
(
)
(
)
(
)
(
)( )
2
212 34kx x x x x x
=
โ+โ โโ
(
)
(
)
(
)
(
)( )
()
2
22
412341lx x x x x x x
=
+โ โโ +