Everything Maths Grade 11

12.2 CHAPTER 12. HYPERBOLIC FUNCTIONS ANDGRAPHS

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(1.) 011q (2.) 011r

Asymptotes EMBBH

There are two asymptotes for functions of the form y =xa+p+ q. They are determined by examining
the domain and range.

We saw that the function was undefined at x =−p and for y = q. Therefore the asymptotes are
x =−p and y = q.

For example, the domain of g(x) =x+1^2 + 2 is{x : x∈R; x�=− 1 } because g(x) is undefined
at x =− 1. We also see that g(x) is undefined at y = 2. Therefore the range is{g(x) : g(x)∈
(−∞;2)∪ (2;∞)}.

From this we deduce that the asymptotes are at x =− 1 and y = 2.

Exercise 12 - 3

1. Given: h(x) =x+4^1 − 2 .Determine the equations of the asymptotes of h.


2. Write down the equation of the vertical asymptote of the graph y =x−^11.

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(1.) 01zd (2.) 01ze

Sketching Graphs of theFormf(x)=

a

x+p

+q EMBBI

In order to sketch graphs of functions of the form, f(x) =x+ap+ q, we need to calculate four charac-
teristics:

1. domain and range


2. asymptotes


3. y-intercept


4. x-intercept