Question

Evaluate the piecewise function at the given values of the independent variable.

f(x) = { 4x + 4 if x < 0, 2x + 5 if x ≥ 0.
(a) f(-3)
(b) f(0)
(c) f(2)

Answer 1

The piecewise function f(x) is evaluated using the appropriate rule for each given value of x. f(-3) equals -8, f(0) equals 5, and f(2) equals 9.

Step-by-step explanation:

To evaluate the piecewise function at the given values, we look at the function f(x) with two different rules depending on the value of x:

• 4x + 4 if x < 0
• 2x + 5 if x ≥ 0

For (a) f(-3), we use the first rule because -3 is less than 0:

f(-3) = 4(-3) + 4 = -12 + 4 = -8

For (b) f(0), we use the second rule because 0 is equal to 0:

f(0) = 2(0) + 5 = 0 + 5 = 5

For (c) f(2), we also use the second rule because 2 is greater than 0:

f(2) = 2(2) + 5 = 4 + 5 = 9