
Vertical, Horizontal & Slant Asymptotes
Presentation
•
Mathematics
•
12th Grade
•
Practice Problem
•
Hard
Standards-aligned
Blakeley Walker
Used 9+ times
FREE Resource
4 Slides • 10 Questions
1
Vertical, Horizontal
& Slant Asymptotes
2
Vertical Asymptotes
A vertical asymptote is a place where the function is undefined and the limit of the function does not exist. However, you can approach one side of the limit which will either approach ∞ or -∞. The factor that does not cancel from the denominator of the function is where the vertical asymptote occurs on the graph.
3
Multiple Choice
Identify all the vertical asymptotes of the function:
f(x)=x2+x−12x2+2x−8
x=−4
x=3
x=4
x=−3
4
Multiple Choice
Evaluate the limit as x→3− of f(x) below:
f(x)=x2+x−12x2+2x−8
0.5
∞
−∞
0
5
Multiple Choice
Evaluate the limit as x→3+ of f(x) below:
f(x)=x2+x−12x2+2x−8
0.5
∞
−∞
0
6
Multiple Choice
Identify the vertical asymptotes:
f(x)=x2−xx3+2x2−24x
x=1
x=−6
x=4
x=0
7
Horiztonal Asymptotes
To find horizontal asymptotes we simply find the limit as we approach either ∞ or -∞. A function can have at most two horizontal asymptotes in either direction of infinite. If the limit approaches a real number, that is where the horizontal asymptote occurs on the y-axis.
8
Multiple Choice
Identify the horizontal asymptote of the function f(x):
f(x)=x2−x−2x2−1
y=−1
y=0
y=2
y=1
9
Multiple Choice
Identify the horizontal asymptote of the function f(x):
f(x)=9x2+1x+2
y=31
y=3
y=0.5
y=0
10
Multiple Choice
Identify the horizontal asymptote of the function f(x):
f(x)=x3+x2−1x2+2
y=0.2
y=3
y=0.5
y=0
11
Slant Asymptotes
A slant asymptote is neither vertical or horizontal because as x approaches ±∞ the limit is also approaching ±∞. Slant asymptotes are also referred to as another name "oblique" asymptotes.
12
Multiple Select
What type of asymptote(s) does this function have?
f(x)=x+5x2−6x+7
Vertical
Horizontal
Slant
13
Multiple Select
What type of asymptote(s) does this function have?
f(x)=3x2−272x2−4x+8
Vertical
Horizontal
Slant
14
Multiple Choice
What type of asymptote(s) does this function have?
f(x)=x2x3−2x2+5
Vertical
Horizontal
Slant
Vertical, Horizontal
& Slant Asymptotes
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