Math112 Practice Test #2

Find the zeros for the polynomial function and give the
multiplicity for each zero. State whether the graph crosses
the x-axis or touches the x-axis and turns around, at each
zero.

Use the Intermediate Value Theorem to show that the
polynomial function has a real zero between the given
integers.

between 1 and 2

Use the Intermediate Value Theorem to determine
whether the polynomial function has a real zero between
the given integers.

between 1 and 2

Graph the polynomial function.

Divide using long division.

Divide using synthetic division.

Use synthetic division and the Remainder Theorem to
find the indicated function value.

Solve the problem.

64) Solve the equation
given that is a root.

Use the Rational Zero Theorem to list all possible rational
zeros for the given function.

Find a rational zero of the polynomial function and use it
to find all the zeros of the function.

Solve the polynomial equation. In order to obtain the first
root, use synthetic division to test the possible rational
roots.

Find an nth degree polynomial function with real
coefficients satisfying the given conditions.

68) n = 3; 3 and i are zeros; f(2) = 30

Factor the polynomial as the product of factors that are
irreducible over the real numbers. Then write the
polynomial in completely factored form involving
complex nonreal, or imaginary numbers.

Find the domain of the rational function.

Find the vertical asymptotes, if any, of the graph of the
rational function.

Find the horizontal asymptote, if any, of the graph of the
rational function.

Use transformations of or to graph the
rational function.

Easier if convert to

Graph the rational function.

Find the indicated intercept(s) of the graph of the
function.

Find the slant asymptote, if any, of the graph of the
rational function.

Answer Key
Test name: 112PRACTICETEST2

1) g(x) and h(x)
2) g(x) and h(x)

7) Yes
8) No
9) Yes


27) (-1, 0) and (-4, 0)
28) (0, 0) and (2, 0)
29) (0, -8)
30) (0, 0)

33) No
34) Yes
35) No
36) Yes
37) 5
38) 4
39) 4
40) not a polynomial function
41) polynomial function
42) polynomial function
43) not a polynomial function
44) 0, touches the x-axis and turns around;
-6, crosses the x-axis
45) 0, crosses the x-axis;
-4, touches the x-axis and turns around;
8, crosses the x-axis
46)
47)
48)
49)
50) x = -1, x = 1, x = - 8
51) 4, multiplicity 1, crosses x-axis; -3, multiplicity 3, crosses x-axis
52) -4, multiplicity 2, touches the x-axis and turns around;
-3, multiplicity 1, crosses the x-axis.
53) f(1) = -5 and f(2) = 292; yes
54) f(1) = 6 and f(2) = -29; yes


71) all real numbers
72) x = 3
73) x = 5, x = 3
74) x = -2
75) y = - 2
76) y = 0
77) y = 1
78) no horizontal asymptote

81) (-9, 0)
82) (6, 0)
83) 0, 1
84) none
85) y = x + 13
86) no slant asymptote