Which of the following polynomials represents a difference of squares? x^2-1,x^2-8,4x^2+16,9x^2-18

Step-by-step explanation:

we know that

Every difference of squares problem can be factored as follows:

If the polynomial represent a difference of squares every number must be a perfect square (Remember that a number is a perfect square if its square root is an integer.)

Verify each case

case 1) we have

In this case both numbers are perfect square

so

therefore

The polynomial represent a difference of squares

case 2) we have

In this case 8 is not a perfect square

therefore

The polynomial not represent a difference of squares

case 3) we have

In this case both numbers are perfect square

but is a sum of squares

therefore

The polynomial not represent a difference of squares

case 4) we have

In this case 2 is not a perfect square

therefore

The polynomial not represent a difference of squares

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: