Everything Maths Grade 10

8.Sketch the functions given and describe the transformation performed on the first function to obtain the

second function. Show all asymptotes.

a)y=

1

x

and

3

x

b)y=

6

x

and

6

x

1

c)y=

5

x

and

5

x

d)y=

1

x

and

1

2 x

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1.2FYH 2.2FYJ 3.2FYK 4.2FYM 5.2FYN 6.2FYP

7.2FYQ 8a.2FYR 8b.2FYS 8c.2FYT 8d.2FYV

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6.5 Exponential functions EMA4V

Functions of the formy=bx EMA4W

Functions of the general formy =abx+qare called exponential functions. In the equationaandqare
constants and have different effects on the function.

Worked example 12: Plotting an exponential function

QUESTION

y=f(x) =bxforb > 0 andb̸= 1

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

f(x) = 2x,g(x) = 3x,h(x) = 5x.

2 1 0 1 2

f(x) = 2x

g(x) = 3x

h(x) = 5x

1.At what point do these graphs intersect?

2.Explain why they do not cut thex-axis.

3.Give the domain and range ofh(x).

4.Asxincreases, doesh(x)increase or decrease?

5.Which of these graphs increases at the slowest rate?

6.Fory=kxandk > 1 , the greater the value ofk, the steeper the curve of the graph. True or false?

Chapter 6. Functions 177