Everything Maths Grade 11

CHAPTER 13. EXPONENTIAL FUNCTIONS AND GRAPHS 13.2

Sketching Graphs of the Form f(x)=

ab

(x+p)

+q

EMBBO

In order to sketch graphs of functions of the form, f(x) = ab(x+p)+ q, we need to determinefour
characteristics:

1. domain and range


2. y-intercept


3. x-intercept

For example, sketch thegraph of g(x) = 3. 2 x+1+ 2. Mark the intercepts.

We have determined thedomain to be{x : x∈R} and the range to be{g(x) : g(x)∈ (2;∞)}.

The y-intercept is yint= 8 and there is no x-intercept.

1

2

3

4

5

6

7

8

9

10

11

4 3 − 2 − − 1 − 1 2 3 4

Figure 13.2: Graph of g(x) = 3. 2 x+1+ 2.

Exercise 13 - 4

1. Draw the graphs of the following on the same set of axes. Label thehorizontal asymptotes and
   y-intercepts clearly.

(a) y = 2x+ 2

(b) y = 2x+2