How is g (x) = x^2-11 related to f (x) = x^2

G (x) x^2-11 is a translation of f (x) x^2 shifted 11 units down

Translation 11 units down

Step-by-step explanation:

Our parent function is f (x) = x². Our new function is g (x) = x² - 11.

This is a type of transformation - a translation specifically. We need to figure out if this is a vertical or a horizontal translation. Vertical transformations alter the entire function while horizontal transformations alter only the x. We see that in g (x), the - 11 is on the entire function (if it was g (x) = (x - 11) ², then it'd be horizontal).

So, since we have "-" 11 and not "+" 11, we know that this is a vertical translation 11 units down.