Everything Maths Grade 10

6.Given the functionsy= 2xandy=

( 1

2

)x

.

a)Draw the graphs on the same set of axes.

b)Is thex-axis an asymptote or an axis of symmetry to both graphs? Explain your answer.

c)Which graph can be described by the equationy= 2x? Explain your answer.

d)Solve the equation 2 x=

( 1

2

)x

graphically and check your answer is correct by using substitution.

7.The curve of the exponential functionfin the accompanying diagram cuts they-axis at the pointA(0; 1)

and passes through the pointB(2; 9).

3 2 (^1) 1 1 2 3
1
2
3
4
5
6
7
8
9
0
A(0; 1)
B(2; 9)
x
y
a)Determine the equation of the functionf.
b)Determine the equation of the functionh(x), the reflection off(x)in thex-axis.
c)Determine the range ofh(x).
d)Determine the equation of the functiong(x), the reflection off(x)in they-axis.
e)Determine the equation of the functionj(x)ifj(x)is a vertical stretch off(x)by+2units.
f)Determine the equation of the functionk(x)ifk(x)is a vertical shift off(x)by 3 units.
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1.2FYX 2.2FYY 3.2FYZ 4.2FZ2 5.2FZ3 6.2FZ4 7.2FZ5
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6.6 Trigonometric functions EMA52
This section describes the graphs of trigonometric functions.
Sine function EMA53
Functions of the formy=sin EMA54
Worked example 16: Plotting a sine graph

QUESTION

y=f() =sin [0° 360 °]

Use your calculator to complete the following table.

Chapter 6. Functions 187