Modulus

Question 1

Modulus or absolute value of a number is

Answer 1

The numbers size written |-1| = 1

Functions can have modulus too.

Question 2

|f(x)| = -f(x) when

Answer 2

F(x) < 0

Question 3

|f(x)| = f(x) when

Answer 3

F(x) => 0

Question 4

Drawing modulus graph y = |f(x)|

Answer 4

Restricts the range to |f(x)| => 0

So reflect the negative part of the line y = f(x) in the x axis

Question 5

Drawing modulus graph y = f(|x|)

Answer 5

The negative x values produce the same result as the positive x values

For negative x values reflect the line in the y axis p28

Question 6

Drawing modulus graph y = |f(-x)|

Answer 6

X values change from positive to negative or from negative to positive.

So graph reflected in y axis. Then any negative values of f(x) are made positive by reflecting them in the x axis.

Question 7

Easiest way to draw modulus graphs

Answer 7

Draw normal graph then reflect line appropriately.

Question 8

If |a| = |b| then

Answer 8

a^2 = b^2

Question 9

If modulus around numbers = something

Answer 9

Then

Numbers without modulus = positive something

Or

Numbers without modulus = negative something

Question 10

Useful rule |x-a| < b

=

Answer 10

a-b