301 Final

Types of Graphs Inverse Functions Logarithms and Exponentials

Horizontal Asymptote. A Horizontal Asymptote is the y-value that a graph approaches as x approaches positive or negative infinity.
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Slant Asymptotes If limx→∞[f(x) − (ax + b)] = 0 or lim x

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

Section 9.2 Continuous Functions; Limits at Infinity

The function f is continuous at x = c if all of the following statements are approaches −1 ... Otherwise y = f(x) has no horizontal asymptotes.

Graphing the curve y =

since the denominator approaches infinity while the numerator is constant. Thus there is no horizontal asymptote approached as x approaches −∞.

301 Final

Horizontal Asymptote: As x approaches infinity or negative infinity Finding Oblique Asymptotes: In the rational function

CHAPTER 13 Limits at Infinity

As x approaches °1 the graph of f (x) becomes ever closer to the horizontal line y = °3

Chapter 5 Section 5

“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.
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Different Types of Limits One-Sided Limits Example Limits at Infinity

One might think that since x2 − 4x − 5 → 0 as x → 5 it would follow that limx→5 If limx→∞ f(x) = L then y = L is a horizontal asymptote.
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1 Limits

10-Oct-2019 Limits at infinity or approaching infinity tell us a lot about the shape of ... This graph has a vertical asymptote at x = 1 a horizontal ...
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2.5 Limits at Infinity

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 

  1. horizontal asymptote limit as x approaches infinity
  2. horizontal asymptote as x approaches negative infinity