Question

Writing an equation for a function after a vertical and horizontal translation please help

Answer 1

`g(x)=-√(x+4)+3`

Explanation:

The function for the graph in blue is given as:

`f(x)=-√(x)`

• A point on f(x) is (0,0).

,

• A corresponding point on g(x), the red graph = (-4, 3)

This means that:

(1) f(x) has been translated by 4 units to the left which gives:

`-√(x+4)`

(2) f(x) has been translated by 3 units up.

`-√(x+4)+3`

Thus, the expression for g(x) is:

`g(x)=-√(x+4)+3`