Everything Maths Grade 10

1.We notice that all graphs pass through the point(0; 1). Any number with exponent 0 is equal to 1.

2.The graphs do not cut thex-axis because you can never get 0 by raising any non-zero number to the

power of any other number.

3.Domain:fx:x 2 Rg

Range:fy:y 2 R; y > 0 g

4.Asxincreases,h(x)increases.

5.f(x) = 2xincreases at the slowest rate because it has the smallest base.

6.True: the greater the value ofk(k >1), the steeper the graph ofy=kx.

 4  3  2  1 1 2 3 4

1

2

3

4

0

F(x)G(x)H(x)

x

y

1.They-intercept is the point(0; 1)for all graphs. For any real numberz:z^0 = 1 z̸= 0.

2.F(x)is the reflection off(x)about they-axis.

3.G(x)is the reflection ofg(x)about they-axis.

4.Domain:fx:x 2 Rg

Range:fy:y 2 R; y > 0 g

5.True: the greater the value ofk(k >1), the steeper the graph ofy=

( 1

k

)x

.

6.The equation of the horizontal asymptote isy= 0, thex-axis.

Functions of the formy=abx+q EMA4X

Investigation: The effects ofa,qandbon an exponential graph.

On the same set of axes, plot the following graphs (a= 1,q= 0andbchanges):

1.y 1 = 2x

2.y 2 =

( 1

2

)x

3.y 3 = 6x

4.y 4 =

( 1

6

)x

2 1 0 1 2

y 1 = 2x

y 2 =

( 1

2

)x

y 3 = 6x

y 4 =

( 1

6

)x

Use your results to deduce the effect ofb.

Chapter 6. Functions 179