Everything Maths Grade 10

Step 3: Determine the asymptote

The horizontal asymptote is the liney= 2.

Step 4: Plot the points and sketch the graph

 4  3  2  1 1 2 3 4

1

2

3

4

5

6

0

y= 3 2 x+ 2

y= 2

(0; 5)

x

y

Domain:fx:x 2 RgRange:fg(x) :g(x)> 2 g

Note that there is no axis of symmetry for exponential functions.

Worked example 15: Sketching an exponential graph

QUESTION

Sketch the graph ofy= 2  3 x+ 6

SOLUTION

Step 1: Examine the standard form of the equation

From the equation we see thata < 0 therefore the graph curves downwards. q > 0 therefore the graph is
shifted vertically upwards by 6 units.

Step 2: Calculate the intercepts

For they-intercept, letx= 0:

y= 2  3 x+ 6

= 2  30 + 6

= 4

This gives the point(0; 4).

For thex-intercept, lety= 0:

y= 2  3 x+ 6

0 = 2  3 x+ 6

6 = 2  3 x

31 = 3x

)x= 1

This gives the point(1; 0).

184 6.5. Exponential functions