draw the graph of the function of F WHOLE x = x - 2
Answers
f(x)=x
x−2
f(x)=(x−2)+2x−2
f(x)=1+2x−2
For vertical asymptotes,
x−2≠0
since the denominator cannot equal to 0 as the function will be undefined at that point. To find at what point the function is undefined, we can go
x−2=0
so
x=2 is our vertical asymptote.
For horizontal asymptotes, we let
x→∞
. As
x→∞, 2x−2→0
. Hence,
f(∞)
f(x)=x
x−2
f(x)=
(x−2)
+
2
x
−
2
f
(
x
)
=
1
+
2
x
−
2
For vertical asymptotes,
x
−
2
≠
0
since the denominator cannot equal to 0 as the function will be undefined at that point. To find at what point the function is undefined, we can go
x
−
2
=
0
so
x
=
2
is our vertical asymptote.
For horizontal asymptotes, we let
x
→
∞
. As
x
→
∞
,
2
x
−
2
→
0
. Hence,
f
(
∞
)
=
1
+
0
=
1
. Therefore, there is an horizontal asymptote at
y
=
1
For intercepts,
When
y
=
0
,
x
=
0
When
x
=
0
,
y
=
0
Plotting your intercepts and drawing in your asymptotes (remember that the asymptotes influence the endpoints of your graph ONLY and nothing else)
graph{x/(x-2) [-10, 10, -5, 5]}=
1
+
0
=
1
. Therefore, there is an horizontal asymptote at
y
=
1
For intercepts,
When
y
=
0
,
x
=
0
When
x
=
0
,
y
=
0
Plotting your intercepts and drawing in your asymptotes (remember that the asymptotes influence the endpoints of your graph ONLY and nothing else)
graph{x/(x-2) [-10, 10, -5, 5]}