Everything Maths Grade 10

Worked example 13: Domain and range of an exponential function

QUESTION

Find the domain and range ofg(x) = 5: 2 x+ 1

SOLUTION

Step 1: Find the domain

The domain ofg(x) = 5 2 x+ 1isfx:x 2 Rg.

Step 2: Find the range

2 x> 0

5  2 x> 0

5  2 x+ 1> 1

Therefore the range isfg(x) :g(x)> 1 g.

Intercepts

They-intercept.

For they-intercept, letx= 0:

y=abx+q

=ab^0 +q

=a(1) +q

=a+q

For example, they-intercept ofg(x) = 5 2 x+ 1is given by settingx= 0:

y= 5 2 x+ 1

= 5 20 + 1

= 5 + 1

= 6

This gives the point(0; 6).

Thex-intercept:

For thex-intercept, lety= 0.

For example, thex-intercept ofg(x) = 5 2 x+ 1is given by settingy= 0:

y= 5 2 x+ 1

0 = 5 2 x+ 1

1 = 5 2 x

2 x=

1

5

There is no real solution. Therefore, the graph ofg(x)does not have anyx-intercepts.

182 6.5. Exponential functions