The graph of $$y=^3\sqrt{x}$$ is shown below. ![](http://admin.getprephub.com/media/editor/te30_20230117200104160505.png) Which of the following is the graph of $$y=2 ^3\sqrt{x-4}$$ ?

The graph of $$y=^3\sqrt{x}$$ can be transformed to get the graph of $$y=^3\sqrt{x-4}$$. Replacing $$x$$ with $$x-4$$ Shifts the graph of $$y=^3\sqrt{x}$$ right by $$4$$ units. ![](http://admin.getprephub.com/media/editor/te30s5_20230117200315370445.png) Multiplying $$^3\sqrt{x-4}$$ by $$2$$ stretches the graph of $$y=^3\sqrt{x-4}$$ vertically by a factor of 2 . ![](http://admin.getprephub.com/media/editor/te30s6_20230117200335527355.png) Before the stretch, the graph passes through $$(-4,-2)$$ after the stretch it passes thrargh $$(-4,-4)$$ So, $$y$$ co-ordinate is multiplied by $$2$$. ![](http://admin.getprephub.com/media/editor/te30s7_20230117200402935449.png)