Everything Maths Grade 10

Complete the following table for each of the functions and draw the graphs on the same system of axes:

F(x) =

(

1

2

)x

,G(x) =

(

1

3

)x

,H(x) =

(

1

5

)x

2 1 0 1 2

F(x) =

( 1

2

)x

G(x) =

( 1

3

)x

H(x) =

( 1

5

)x

1.Give they-intercept for each function.

2.Describe the relationship between the graphsf(x)andF(x).

3.Describe the relationship between the graphsg(x)andG(x).

4.Give the domain and range ofH(x).

5.Fory=

(

1

k

)x

andk > 1 , the greater the value ofk, the steeper the curve of the graph. True or false?

6.Give the equation of the asymptote for the functions.

SOLUTION

Step 1: Substitute values into the equations
2 1 0 1 2
f(x) = 2x

1

4

1

2

1 2 4

g(x) = 3x

1

9

1

3

1 3 9

h(x) = 5x

1

25

1

5

1 5 25

2 1 0 1 2

F(x) =

( 1

2

)x

4 2 1

1

2

1

4

G(x) =

( 1

3

)x

9 3 1

1

3

1

9

H(x) =

( 1

5

)x

25 5 1

1

5

1

25

Step 2: Plot the points and join with a smooth curve

 4  3  2  1 1 2 3 4

1

2

3

4

0

h(x)g(x)f(x)

x

y

178 6.5. Exponential functions