Evaluate the function at each specified value of the independent variable and simplify.

Question

f(x) = {2x + 1, x < 0

{2x + 2, x ≥ 0

(A) f(-1) (B) f(0) (C) f(2)

Answer 1

Hi Ayanna!

This is a piecewise function, which means the way the function works at each value of the independent variable can be differerent. Our independent variable is x. You can remember that by thinking "I choose the independent variable" and then the function determines the f(x) value based on what I choose. You can also remember "in"dependent is the input, and f(x), the function value, is the output.

(A) For f(-1), we will use f(x) = 2x + 1 since -1 < 0. f(-1) = 2(-1) +1 = -1.

(B) For f(0), we will use f(x) = 2x + 2 since 0 ≥ 0. f(0) = 2(0) +2 = 2.

(C) For f(2), we will use f(x) = 2x + 2 since 2 ≥ 0. f(2) = 2(2) +2 = 6.