What is Modulus?
Simply, it is the non-negative value of x without regards to the sign.
The modulus of x can be written as |x|.
The sign is always ignored and the output is ALWAYS POSITIVE.
E.g
|-5.2|= 5.2 |8.5|= 8.5
,This can be seen on a graph…
y=x y = |x|
y
y
x x
Here we are reflecting the negative values of f(x) in the x axis.
,Q1
a) Draw a sketch of y= | 2x + 4|
b) Hence, solve the equation | 2x + 4| = 6
,Q2
a) Draw a sketch of y = | 2x-8 | and on the same axes the graph y= x + 2
b) Hence, solve the equation | 2x-8 | = x + 2
,Q3
Shown here is a sketch of y = f(x), where f (x) = | x + 1 | - 2
a) Find the coordinates of the points P, Q and R.
y
x
P R
Q
b) Sketch the graph y = |f(x)|
c) Solve | f (x) | = 2x
,
Simply, it is the non-negative value of x without regards to the sign.
The modulus of x can be written as |x|.
The sign is always ignored and the output is ALWAYS POSITIVE.
E.g
|-5.2|= 5.2 |8.5|= 8.5
,This can be seen on a graph…
y=x y = |x|
y
y
x x
Here we are reflecting the negative values of f(x) in the x axis.
,Q1
a) Draw a sketch of y= | 2x + 4|
b) Hence, solve the equation | 2x + 4| = 6
,Q2
a) Draw a sketch of y = | 2x-8 | and on the same axes the graph y= x + 2
b) Hence, solve the equation | 2x-8 | = x + 2
,Q3
Shown here is a sketch of y = f(x), where f (x) = | x + 1 | - 2
a) Find the coordinates of the points P, Q and R.
y
x
P R
Q
b) Sketch the graph y = |f(x)|
c) Solve | f (x) | = 2x
,
