Question

Y=x^2 how does Y= (x-4^2) andY = (x+3) differ from theParent function and each other?what causes this to change?

Answer 1

The parent function is:

y = x²

This is a quadratic function

The child functions are:

y = x - 4² whcih can be written as

y = x - 16

The second child function is

y = x + 3

The two child functions are linear functions while the parent function is a quadratic function.

The parent and child functions also differ in their ranges and domains

For y = x²

Domain = ( -∞ , ∞ )

Range = [0 , ∞ )

For y = x - 4² and y = x + 3:

Domain = ( -∞ , ∞ )

Range = (-∞ , ∞ )

The difference between y = x - 4² and y = x + 3 is their intercepts on the y axis .

For y = x - 4², the y - intercept is -16

For y = x + 3, the y - intercept 3

This change is due to transformation (basically translation) on the x and y axes