This preview shows page 1. Sign up to view the full content.
Unformatted text preview: tote of the graph of a function
y = f (x) if as x → c− or as x → c+ , either f (x) → ∞ or f (x) → −∞.
3 We would need Calculus to conﬁrm this analytically.
Here, the word ‘larger’ means larger in absolute value. 4.1 Introduction to Rational Functions 235 Definition 4.3. The line y = c is called a horizontal asymptote of the graph of a function
y = f (x) if as x → −∞ or as x → ∞, either f (x) → c− or f (x) → c+ .
In our discussion following Example 4.1.1, we determined that, despite the fact that the formula for
h(x) reduced to the same formula as f (x), the functions f and h are diﬀerent, since x = 1 is in the
domain of f , but x = 1 is not in the domain of h. If we graph h(x) = 2x2 −11 − 3x−1 using a graphing
calculator, we are surprised to ﬁnd that the graph looks identical to the graph of y = f (x). There
is a vertical asymptote at x = −1, but near x = 1, everything seem ﬁne. Tables of values provide
numerical evidence which supports...
View Full Document