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Rule A (x, y) → (x, -y) describes the transformation.

Step-by-step explanation:

Step 1; To understand reflection across an axis we need to be able to know which quadrant the shape is already in and in which quadrant it will be in after reflection. The given shape is currently in the fourth quadrant where the points in it will have a positive x coordinate and a negative y coordinate. So assume the values are in the format of (x, y).

Step 2; Due to reflection across the x-axis, the shape will be reflected in the first quadrant. In this, the x and y coordinates both have a positive value. So due to reflection, the x value remains unchanged while the y value is the same but it has the opposite symbol i.e. negative. So if the shape had a value of (x, y) due to reflection it would have (x, -y).

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: