In the second case the graph flattens out on the left
limits at infinity
“y approaches negative infinity as x approaches 0 from the left” The line y = b is a horizontal asymptote of the function y = f (x) if.
math rational functions
Horizontal Asymptotes. Geometrically lim x→+∞ f(x) = L means that the graph of f(x) approaches the horizontal line y = L at infinity
RGASC CMath Limits as x approaches Infinity
Horizontal Asymptote: As x approaches infinity or negative infinity Finding Oblique Asymptotes: In the rational function
Therefore the graph of y = 2 + 10>x2 approaches the horizontal asymptote y = 2 as x S ∞ and as x S - ∞ (Figure 2.32). b. The numerator of sin x> 1x is
SE C S
What about analytically finding horizontal asymptotes? When x approaches infinity or negative infinity the numerator and denominator will take the form.
. limits involving infinity p.
since the denominator approaches infinity while the numerator is constant. Thus there is no horizontal asymptote approached as x approaches −∞.
If n < m then the x-axis is the horizontal asymptote. When a>b
Situation Rational Functions
Horizontal Asymptote. A Horizontal Asymptote is the y-value that a graph approaches as x approaches positive or negative infinity.
f(x) approaches the graph of the line y = ax + b as x approaches ∞. [ Note: If a = 0 this is a horizontal asymptote]. In the case of rational functions
. Summary of Curve Sketching
- horizontal asymptote limit as x approaches infinity
- horizontal asymptote as x approaches negative infinity