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

Question

f(x) = {x² + 2, x ≤ 1

{2x² + 2, x > 1

(a) f(-2) (b) f(1) (c) f(2)

Answer 1

An independent variable is the one you choose the value of. Usually, that's x. The function output is f(x). You can remember input = independent. So f(x) for x = - 2 is f(-2), To determine which function we use for a given input here, we look at where it falls on the piecewise definition. The first two x-values (-2 and 1) use the first function, f(x) = x² + 2 because they are both equal or less than 1, and the third x-value (2) uses the third function 2x² + 2 because it is greater than one.

a: f(-2) = (-2)² + 2 = 6

b: f(1) = (1)² + 2 = 3

c: f(2) = 2(2)² + 2 = 10