Which of the four statements is true and also write a one-step inequality as an example of when you would "flip" the sign.

Step-by-step explanation:

There are 5 types of Inequality sign :

1. = read  '' equals to ''

2. > read '' greater than ''

3. < read '' less than ''

4. ≥ read '' greater than or equals to ''

5. ≤ read '' less than or equals to ''

Example -

1. 2 = 3   ( 2 is equals to 3 )

2. 3 > 2 ( 3 is greater than 2 )

3. 2< 4  ( 2 is less than 4 )

4. 3 ≥ 2 ( 3 is greater than or equals to 2)

5. 2 ≤ 4 ( 2 is less than or equals to 4 )

One - step inequality :

Addition and Subtraction Properties of Inequality -

If a > b, then a + c > b + c

If a > b, then a − c > b − c

Multiplication and Division Properties of Inequality -

If a > b, then ac > bc, if c > 0

If a > b, then ac < bc, if c < 0

If a > b, then , if c > 0

If a > b, then ,, if c < 0

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: