This was part of the question. the entire question was 1) find all solutions of the equation algebraically 2) then, check your solution both algebraically and graphically.
I understood how to do the first part but i didn't know how to graph it (2nd part)?
The next step, assuming you have the correct solution, is to graph not the solution but the original function -- y = (2x + 5)^(1/3) + 3 -- and check that the ordered pair (x,0) on the graph matches your solution. You don't need to solve anything to graph the function, since it is already in the form f(x)=x. There are two ways to go about graphing it: transformations of the graph of
f(x) = x^(1/3), which is the more formal way; or by just plugging in values for x and finding the corresponding values for y and drawing a smooth curve between those points.
Well, the principles of transformation apply to any graph, but that is still sort of the involved way to do this if you are not that familiar with transformations. In order to draw a graph, all you really need is a set of ordered pairs (x,y) for which the equation is true. You find those by solving the equation for a series of values of x over the range where you want to draw the graph.
Plug in values for x and solve for y, but yes, that will generate a set of ordered pairs you can use to draw the graph. It helps if you know the general shape you are going for, so if you have a graphing calculator you can plug in the equation to see the general shape. And yes, I can help you with the next one.