Answers and Explanations 155
Answers
1–100
73.
y
x
= −
+
1
5
3
To stretch the graph of y x
=
horizontally by a factor of 5, replace x with 1
5
x to get
y
x
= 1
5
. Next, to reflect the graph of y
x
= 1
5
across the x-axis, multiply the right side
of the equation y
x
= 1
5
by –1 to get y
x
= − 1
5
. Last, to shift the graph of y
x
= − 1
5
up 3
units, add 3 to the right side of the equation to get
y
x
= −
+
1
5
3
74.
f x
x
x
x
( ) = −
−
−
+
3
8
15
8
3
4
3
3
2
The polynomial has x intercepts at x = –4, x = –2, and x = 1, so you know that the
polynomial has the factors (x + 4), (x + 2), and (x – 1). Therefore, you can write
f x
a x
x
x
( )
(
)(
)(
)
=
+
+
−
4
2
1
Use the point (0, 3) to solve for a:
3
0 4 0 2 0 1
3
8
3
8
=
+
+
−
= −
− =
a
a
a
(
)(
)(
)
Now you can enter the value of a in the equation of the polynomial and simplify:
f x
x
x
x
x
x
x
x
x
x
x
( )
(
)(
)(
)
(
)
= −
+
+
−
= −
+
+
(
) −
= −
− +
−
+
3
8
4
2
1
3
8
6
8
1
3
8
6
6
2
3
2
2
8 8
8
3
8
5
2
8
3
8
15
8
3
4
3
3
2
3
2
x
x
x
x
x
x
x
−
(
)
= −
+
+
−
(
)
= −
−
−
+
Here’s the graph of f x
x
x
x
( ) = −
−
−
+
3
8
15
8
3
4
3
3
2
: