Everything Maths Grade 11

CHAPTER 13. EXPONENTIAL FUNCTIONS AND GRAPHS 13.2

If a < 0 then:

b(x+p) > 0

a. b(x+p) < 0

a. b(x+p)+ q < q

f(x) < q

Therefore, if a < 0 , then the range is{f(x) : f(x)∈ (−∞; q]}.

For example, the domain of g(x) = 3. 2 x+1+ 2 is{x : x∈R}. For the range,

2 x+1 > 0

3. 2 x+1 > 0

3. 2 x+1+ 2 > 2

Therefore the range is{g(x) : g(x)∈ [2;∞)}.

Exercise 13 - 1

1. Give the domain of y = 3x.


2. What is the domain and range of f(x) = 2x?


3. Determine the domain and range of y = (1,5)x+3.

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

(1.) 011z (2.) 0120 (3.) 0121

Intercepts EMBBM

For functions of the form, y = ab(x+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.

The y-intercept is calculated as follows:

y = ab(x+p)+ q (13.1)

yint = ab(0+p)+ q (13.2)

= abp+ q (13.3)

For example, the y-intercept of g(x) = 3. 2 x+1+ 2 is given by setting x = 0 to get:

y = 3. 2 x+1+ 2

yint = 3. 2 0+1+ 2

= 3. 21 + 2

= 3 .2 + 2

= 8