Answers and Explanations 157
Answers
1–100
77.
f x
x
x
( ) =
+
+
3
2
15
24
2
The parabola has x-intercepts at x = –8 and x = –2, so you know that (x + 8) and (x + 2)
are factors of the parabola. Therefore, you can write
f x
a x
x
( )
(
)(
)
=
+
+
8
2
Use the point (–4, –12) to solve for a:
− = − +
− +
− =
−
− = −
=
12
4 8
4 2
12
4
2
12
8
3
2
a
a
a
a
(
)(
)
( )( )
Now you can enter the value of a in the equation of the parabola and simplify:
f x
x
x
x
x
x
x
( )
(
)(
)
=
+
+
=
+
+
(
)
=
+
+
3
2
8
2
3
2
10 16
3
2
15
24
2
2
78.
domain: [–2, ∞); range: [1, ∞)
The function is continuous on its domain.
The lowest x coordinate occurs at the point (–2, 3), and then the graph extends indefinitely to the right; therefore, the domain is [–2, ∞). The lowest y coordinate occurs at
the point (–1, 1), and then the graph extends indefinitely upward; therefore, the range
is [1, ∞).
Note that the brackets in the interval notation indicate that the value –2 is included in
the domain and that 1 is included in the range.
79.
domain: [–5, 3]; range: [–2, 2]
Notice that the function is continuous on its domain.
The smallest x coordinate occurs at the point (–5, 0), and the largest x coordinate
occurs at the point (3, 0); therefore, the domain is [–5, 3]. The smallest y coordinate
occurs at the point (1, –2), and the largest y coordinate occurs at the point (–3, 2);
therefore, the range is [–2, 2].
Note that the brackets in the interval notation indicate that the values –5 and 3 are
included in the domain and that the values –2 and 2 are included in the range.