Everything Maths Grade 10

Asymptotes

Exponential functions of the formy=abx+qhave a single horizontal asymptote, the linex=q.

Sketching graphs of the formy=abx+q EMA4Z

In order to sketch graphs of functions of the form,y=abx+q, we need to determine four characteristics:

1.sign ofa

2.y-intercept

3.x-intercept

4.asymptote

VISIT:

The following video shows some examples of sketching exponential functions.

See video:2FYWatwww.everythingmaths.co.za

Worked example 14: Sketching an exponential function

QUESTION

Sketch the graph ofg(x) = 3 2 x+ 2. Mark the intercept and the asymptote.

SOLUTION

Step 1: Examine the standard form of the equation

From the equation we see thata > 1 , therefore the graph curves upwards.q > 0 therefore the graph is shifted

vertically upwards by 2 units.

Step 2: Calculate the intercepts

For they-intercept, letx= 0:

y= 3 2 x+ 2

= 3 20 + 2

= 3 + 2

= 5

This gives the point(0; 5).

For thex-intercept, lety= 0:

y= 3 2 x+ 2

0 = 3 2 x+ 2

2 = 3 2 x

2 x=

2

3

There is no real solution, therefore there is nox-intercept.

Chapter 6. Functions 183