Question

if you horizontally shift the square root parent function, F(x) = la1" title="\sqrt{x}" alt="\sqrt{x}" align="absmiddle" class="latex-formula">, left four units, what is the equation of the new function?

Answer 1

ANSWER

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

EXPLANATION

The parent square root function is

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

The translation

$g(x ) = \sqrt{x + k}$

Will shift the graph of f(x) k units to left.

The translation

$g(x) = \sqrt{x -k}$

will shift the graph of f(x) to the right by k units.

Therefore if f(x) is shifted 4 units to the left its new equation is:

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