IMathAS-libretexts

Suppose $\displaystyle {f{{\left({x}\right)}}}=\sqrt{{{x}}}$ . Give the function for each of the following transformations.

The graph of $\displaystyle {f{{\left({x}\right)}}}$ reflected across the x-axis.

$\displaystyle {f{{\left({x}\right)}}}=-\sqrt{{-{x}}}$
$\displaystyle {f{{\left({x}\right)}}}=-\sqrt{{{x}}}$
$\displaystyle {f{{\left({x}\right)}}}=\sqrt{{-{x}}}$

The graph of $\displaystyle {f{{\left({x}\right)}}}$ shifted right 4 units

$\displaystyle {f{{\left({x}\right)}}}=\sqrt{{{x}-{4}}}$
$\displaystyle {f{{\left({x}\right)}}}=\sqrt{{{x}}}-{4}$
$\displaystyle {f{{\left({x}\right)}}}=\sqrt{{{x}+{4}}}$
$\displaystyle {f{{\left({x}\right)}}}=\sqrt{{{x}}}+{4}$

The graph of $\displaystyle {f{{\left({x}\right)}}}$ shifted up 5 units

$\displaystyle {f{{\left({x}\right)}}}=\sqrt{{{x}+{5}}}$
$\displaystyle {f{{\left({x}\right)}}}=\sqrt{{{x}}}+{5}$
$\displaystyle {f{{\left({x}\right)}}}=\sqrt{{{x}-{5}}}$
$\displaystyle {f{{\left({x}\right)}}}=\sqrt{{{x}}}-{5}$

The graph of $\displaystyle {f{{\left({x}\right)}}}$ shifted right 5 units and shifted down 3 units.

$\displaystyle {f{{\left({x}\right)}}}=\sqrt{{{x}-{5}}}+{3}$
$\displaystyle {f{{\left({x}\right)}}}=\sqrt{{{x}+{5}}}-{3}$
$\displaystyle {f{{\left({x}\right)}}}=\sqrt{{{x}+{5}}}+{3}$
$\displaystyle {f{{\left({x}\right)}}}=\sqrt{{{x}-{5}}}-{3}$