Chapter 2: Functions and Graphs
The modulus function (absolute value)
The modulus of a number a, written as |𝑎|, is a non-negative numerical value.
Example 1: Write down the values of
a) |−5| =
b) |2.5| =52.5
A modulus function is, in general, a function of the type 𝑦 = |𝑓(𝑥)|
𝑓 (𝑥 ), 𝑓(𝑥) ≥ 0
|𝑓(𝑥)| =
−𝑓(𝑥 ), 𝑓(𝑥) < 0
To sketch the graph of 𝑦 = |𝑎𝑥 + 𝑏|, sketch 𝑦 = 𝑎𝑥 + 𝑏 then reflect the
section of the graph below the x-axis in the x-axis.
Example 2: Sketch the graph of 𝑦 = |2𝑥 + 3|
3
1ˢᵗ sketchy 2
If
E
22 31 7
check X 2 9
3
1 I
, Example 3: Sketch the graph of 𝑦 = |𝑥 − 3𝑥 − 4|
4
1ˢᵗ sketch y x 3
s o
9 4
In ILM
4,0
Solving equations with modulus
to Example 4: Solve the equation |2𝑥 − 1| = 5
1
9 2
F
9
51 x f
EEEE 2x
t5
qq.fi 51
The modulus function (absolute value)
The modulus of a number a, written as |𝑎|, is a non-negative numerical value.
Example 1: Write down the values of
a) |−5| =
b) |2.5| =52.5
A modulus function is, in general, a function of the type 𝑦 = |𝑓(𝑥)|
𝑓 (𝑥 ), 𝑓(𝑥) ≥ 0
|𝑓(𝑥)| =
−𝑓(𝑥 ), 𝑓(𝑥) < 0
To sketch the graph of 𝑦 = |𝑎𝑥 + 𝑏|, sketch 𝑦 = 𝑎𝑥 + 𝑏 then reflect the
section of the graph below the x-axis in the x-axis.
Example 2: Sketch the graph of 𝑦 = |2𝑥 + 3|
3
1ˢᵗ sketchy 2
If
E
22 31 7
check X 2 9
3
1 I
, Example 3: Sketch the graph of 𝑦 = |𝑥 − 3𝑥 − 4|
4
1ˢᵗ sketch y x 3
s o
9 4
In ILM
4,0
Solving equations with modulus
to Example 4: Solve the equation |2𝑥 − 1| = 5
1
9 2
F
9
51 x f
EEEE 2x
t5
qq.fi 51
