Answer:
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.
