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
