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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

1 Answer

5 votes
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

User Josh Blade
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