What is the value f(-4)? {-10 if x < -5 {x cubed if -5 less than or equal to x less than or equal to < 2 {2x + 4 if x > 2 a. -10 b. -12 c. -64 d. -4

choice C) -64




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



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

The number line shows negative and positive numbers

Step-by-step explanation: