Which graph represents the function f (x) = -^3√x+1-2?

A

Step-by-step explanation:

Unfortunately, your f (x) = -^3√x+1-2 is not properly formed.  I am assuming that you actually meant f (x) = -3√(x+1) - 2.  In this case you can see the basic function g(x) = √x, whose graph passes through the point (0, 0) and increases as x increases.

The graph of h(x) = -√x also passes thru (0, 0), but decreases as x increases.

If we replace the 'x' in h(x) with 'x+1,' the effect on the graph is to translate it 1 unit to the left.  If you then append "-2," the effect on the graph is to translate it downward by 2 units.

What's the y-intercept of f(x) = -3√(x+1) - 2?  To answer this, set x = 0 and solve for y:   f(0) = -3√(0+1) - 2, or -3(1) - 2, or -5.

Note that -5 is the algebraically smallest y value that we could have.  That automatically points to Answer choice A.  In Answer choice A, note that the  whole graph of -3√(x+1) has been shifted to the left by one unit.  This also confirms the Answer Choice A is the correct one.