Everything Maths Grade 11

12.2 CHAPTER 12. HYPERBOLIC FUNCTIONS ANDGRAPHS

Domain and Range EMBBF

For y =xa+p+ q, the function is undefined for x =−p. The domain is therefore
{x : x∈R,x�=−p}.

We see that y =x+ap+ q can be re-written as:

y =

a

x + p

+ q

y− q =

a

x + p

If x�=−p then: (y− q)(x + p) = a

x + p =

a

y− q

This shows that the function is undefined at y = q. Therefore the rangeof f(x) = xa+p+ q is
{f(x) : f(x)∈ R, f(x)�= 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.

y =

2

x + 1

+ 2

(y− 2) =

2

x + 1

(y− 2)(x + 1) = 2

(x + 1) =

2

y− 2

We see that g(x) is undefined at y = 2. Therefore the range is{g(x) : g(x)∈ (−∞;2)∪ (2;∞)}.

Exercise 12 - 1

1. Determine the rangeof y =x^1 + 1.


2. Given:f(x) =x−^88 + 4. Write down the domain of f.


3. Determine the domain of y =−x+1^8 + 3

More practice video solutions or help at http://www.everythingmaths.co.za

(1.) 01za (2.) 01zb (3.) 01zc

Intercepts EMBBG

For functions of the form, y =xa+p+ q, the intercepts with the x and y axis are calculated by setting
x = 0 for the y-intercept and by setting y = 0 for the x-intercept.