Construct a function whose reflection in the line of y=x is itself. state the symmetries of the function.

ANSWER TO PART A

The mapping for the reflection in the line , is given by

.

That is the coordinates swap position .

The only way we can construct a function , such that;

are equal is when

.

So that when .

The mapping then becomes

.

Therefore the function, is the function whose reflection in the line

is itself.

ANSWER TO PART B

The function is symmetrical with respect to the origin. That is to say the function is an odd function.

A function is symmetric with respect to the origin, if it satisfies the condition,

For instance,

Since

We say the function is symmetric with respect to the origin.

h= 12 inches

step-by-step explanation: