Answer: choice C) -64
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This is a piecewise function. The function f(x) will change based on what x happens to be. There are 3 different cases here
Case A: f(x) = -10
Case A is only true if x < -5
Case B: f(x) = x^3
Case B is only true if -5 <= x <= 2
The symbol "<=" without quotes means "less than or equal to"
and finally,
Case C: f(x) = 2x+4
Case C is only true if x > 2
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We want to find the value of f(-4) meaning we want to find the value of f(x) when x = -4
Look through the inequalities and see where x = -4 fits
does x = -4 make x < -5 true? In other words, is -4 smaller than -5? In other words is -4 to the left of -5? The answer to all of these questions is a simple "no"
So we move on. Check the second inequality -5 <= x <= 2 and sure enough -4 is between those two endpoints. So we'll use the second function
We will use f(x) = x^3
f(x) = x^3
f(-4) = (-4)^3 .... every x has been replaced with -4
f(-4) = (-4)*(-4)*(-4) ... expand out the cubic
f(-4) = ((-4)*(-4))*(-4)
f(-4) = (16)*(-4)
f(-4) = -64
Which is our final answer