Question

A piecewise-defined function has different rules for different parts, or pieces, of its
domain. In order to evaluate a piecewise defined function for a given value of x
find the interval, or piece, that y belongs to. Find the corresponding definition at
the function for that interval

Answer 1

Applying the piecewise function, we have that:

a) $f(-5) = 3$

b) $f(-4) = 3$

c) $f(-3) = 3$

d) $f(-2) = -4$

e) $f(-1) = -3$

f) $f(0) = -2$

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The function is:

$f(x) = 3, -5 \leq x < -2$

$f(x) = x - 2, -2 \leq x \leq 0$

For items a, b and c, the input x is values between -5 and -2, thus, the definition is:

$f(x) = 3$

Then

$f(-5) = 3$

$f(-4) = 3$

$f(-3) = 3$

For items d, e and f, values of x between -2 and 0, thus, the definition is:

$f(x) = x - 2$

Then

$f(-2) = -2 - 2 = -4$

$f(-1) = -1 - 2 = -3$

$f(0) = 0 - 2 = -2$

A similar problem is given at https://brainly.com/question/24815096