For the function find any horizontal, slant, or curvilinear asymptotes. Specify the type of each asymptote, and whether the function f approaches the asymptote as x approaches ∞, -∞, or both.
f(x) = 2-x
Answer
horizontal asymptote at y = 0. f approaches the asymptote as x approaches ∞
Example 2
For the function find any horizontal, slant, or curvilinear asymptotes. Specify the type of each asymptote, and whether the function f approaches the asymptote as x approaches ∞, -∞, or both.
Answer
slant asymptote at y = x + 3. f approaches the asymptote as x approaches ∞ or -∞
Example 3
For the function find any horizontal, slant, or curvilinear asymptotes. Specify the type of each asymptote, and whether the function f approaches the asymptote as x approaches ∞, -∞, or both.
f(x) = 3 + ex
Answer
horizontal asymptote at y = 3. f approaches the asymptote as x approaches -∞
Example 4
For the function find any horizontal, slant, or curvilinear asymptotes. Specify the type of each asymptote, and whether the function f approaches the asymptote as x approaches ∞, -∞, or both.
Answer
horizontal asymptote at y = 4. f approaches the asymptote as x approaches ∞ or -∞
Example 5
For the function find any horizontal, slant, or curvilinear asymptotes. Specify the type of each asymptote, and whether the function f approaches the asymptote as x approaches ∞, -∞, or both.
Answer
curvilinear asymptote at y = 3x2 – 17. f approaches the asymptote as x approaches ∞ or -∞
Example 6
Find the horizontal / slant / curvilinear asymptote for the rational function.
Answer
horizontal asymptote at
Example 7
Find the horizontal / slant / curvilinear asymptote for the rational function.
Answer
horizontal asymptote at y = 0
Example 8
Find the horizontal / slant / curvilinear asymptote for the rational function.
Answer
horizontal asymptote at y = 11
Example 9
Find the horizontal / slant / curvilinear asymptote for the rational function.
Answer
slant asymptote at y = 3x – 12.
Example 10
Find the horizontal / slant / curvilinear asymptote for the rational function.
