Everything Maths Grade 11

CHAPTER 12. HYPERBOLIC FUNCTIONS ANDGRAPHS 12.2

The y-intercept is calculated as follows:

y =

a

x + p

+ q (12.1)

yint =

a

0 + p

+ q (12.2)

=

a

p

+ q (12.3)

For example, the y-intercept of g(x) =x^2 +1+ 2 is given by setting x = 0 to get:

y =

2

x + 1

+ 2

yint =

2

0 + 1

+ 2

=

2

1

+ 2

= 2 + 2

= 4

The x-intercepts are calculated by setting y = 0 as follows:

y =

a

x + p

+ q (12.4)

0 =

a

xint+ p

+ q (12.5)

a

xint+ p

=−q (12.6)

a =−q(xint+ p) (12.7)

xint+ p =

a

−q

(12.8)

xint =

a

−q

− p (12.9)

For example, the x-intercept of g(x) =x+1^2 + 2 is given by setting x = 0 to get:

y =

2

x + 1

+ 2

0 =

2

xint+ 1

+ 2

−2 =

2

xint+ 1

−2(xint+ 1) = 2

xint+ 1 =

2

− 2

xint =− 1 − 1

xint =− 2

Exercise 12 - 2

1. Given: h(x) =x+4^1 − 2. Determine the coordinates of the intercepts of h with the x- and y-axes.


2. Determine the x-intercept of the graph of y =^5 x+2. Give the reason why there is no y-intercept
   for this function.