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Chapter
3
300
Functions and Their Graphs
3.2
The Graph of a Function
1.
x
2
+
4
y
2
=
16
x
intercepts:
x
2
+
4 0
( 29
2
=
16
⇒
x
2
=
16
⇒
x
= ±
4
⇒ 
4,0
( 29
, 4,0
( 29
y
intercepts:
0
( 29
2
+
4
y
2
=
16
⇒
4
y
2
=
16
⇒
y
2
=
4
⇒
y
= ±
2
⇒
0,

2
( 29
, 0,2
( 29
2.
False
3.
vertical
4.
f
5
( 29
= 
3
5.
f x
( 29
=
ax
2
+
4
a

1
( 29
2
+
4
=
2
⇒
a
= 
2
6.
False
7.
False
8.
True
9.
(a)
f
(0)
=
3 since (0,3) is on the graph.
f
(

6)
= 
3 since (

6,

3) is on the graph.
(b)
f
(6)
=
0 since (6,0) is on the graph.
f
(11)
=
1 since (11,1) is on the graph.
(c)
f
(3) is positive since
f
(3)
≈
3.7.
(d)
f
(

4) is negative since
f
(

4)
≈ 
1.
(e)
f
(
x
)
=
0 when
x
= 
3,
x
=
6, and
x
=
10.
(f)
f
(
x
)
0 when

3
<
x
<
6, and 10 <
x
≤
11.
(g)
The domain of
f
is
x

6
≤
x
≤
11
{ }
or

6,11
[ ]
(h)
The range of
f
is
y

3
≤
y
≤
4
{ }
or

3,4
[ ]
(i)
The
x
intercepts are (–3, 0), (6, 0), and (11, 0).
(j)
The
y
intercept is (0, 3)
(k)
The line
y
=
1
2
intersects the graph 3 times.
(l)
The line
x
=
5 intersects the graph 1 time
(m)
f
(
x
)
=
3 when
x
=
0 and
x
=
4.
(n)
f
(
x
)
= 
2 when
x
= 
5 and
x
=
8.
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View Full DocumentSection 3.2
The Graph of a Function
301
10.
(a)
f
(0)
=
0 since (0,0) is on the graph.
f
(6)
=
0 since (6,0) is on the graph.
(b)
f
(2)
= 
2 since (2,

2) is on the graph.
f
(

2)
=
1 since (

2,1) is on the graph.
(c)
f
(3) is negative since
f
(3)
≈ 
1.
(d)
f
(

1) is positive since
f
(

1)
≈ 
0.4.
(e)
f
(
x
)
=
0 when
x
=
0,
x
=
4, and
x
=
6.
(f)
f
(
x
)
<
0 when 0
<
x
<
4.
(g)
The domain of
f
is
x

4
≤
x
≤
6
{ }
or

4,6
[ ]
(h)
The range of
f
is
y

2
≤
y
≤
3
{ }
or

2, 3
[ ]
(i)
The
x
intercepts are (0, 0), (4, 0), and (6, 0).
(j)
The
y
intercept is (0, 0).
(k)
The line
y
=
1 intersects the graph 2 times.
(l)
The line
x
=
1 intersects the graph 1 time.
(m)
f
(
x
)
=
3 when
x
=
5.
(n)
f
(
x
)
= 
2 when
x
=
2.
11.
Not a function since vertical lines will intersect the graph in more than one point.
12.
Function
(a)
Domain:
x x
is any real number
{ }
;
Range:
y y
0
{ }
(b)
intercepts: (0,1)
13.
Function
(a)
Domain:
x
π≤
x
≤π
{ }
;
Range:
y

1
≤
y
≤
1
{ }
(b)
intercepts:

π
2
,0
,
π
2
,0
, (0,1)
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 Spring '08
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 Algebra, YIntercept

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