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)

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asked Mar 7, 2024 40.9k views

1 Answer

Ernesto Badillo · Answer 1 · 2024-03-12T23:06:31+0000

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.

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:

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