Question

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

Answer 1

Translation 11 units down

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.

Answer 2

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