Question

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

Answer 1

Answer:

$g(x)=-\sqrt{x+4}+3$

Explanation:

The function for the graph in blue is given as:

$f(x)=-\sqrt{x}$

• 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:

$-\sqrt{x+4}$

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

$-\sqrt{x+4}+3$

Thus, the expression for g(x) is:

$g(x)=-\sqrt{x+4}+3$