The graph of [tex]y= \sqrt[3]{x} [/tex] was shifted 5 units down and 4 units to the left. What is the equation of the resulting graph?Please answer quickly!
Accepted Solution
A:
We have as our parent function [tex]y= \sqrt[3]{x} [/tex]. To shift the graph horizontally by c units, we have to put c inside the parentheses, that is, under the cube-root. Now, we want to move the graph four units to the left. To do that, we write [tex]y= \sqrt[3]{x+4}[/tex]. Notice that we put +4, and not –4. That may seem a bit counterintuitive, but think that the value that gave some f(x) in the original function must now be four more than it to get the same value. If that explanation confuse you, don't worry; just remember for the horizontal shift it's the opposite sign.
The easiest step is applying the vertical shift. Every value f(x) must be shifted up by 5 units. The way to do this? Just add +5 outside of the parentheses.
In final form, you have [tex]y= \sqrt[3]{x+4}+5 [/tex].