5 Determine whether each of the following functions is even

5. Determine whether each of the following functions is even, odd, or neither. Must show how you tested it in order to get credit.   

Solution

Solution:

Given Equations

f(x) = 4/5x - 10

f(- x) = 4/5(- x) - 10

f(- x) = - 4/5x - 10

f(- x) = - (4/5x + 10)

Note: The first one term in f(x) changed signs when x was replaced with (-x),

but the (constant) term did not . So the resulting f(-x) is not equal to f(x) or -f(x). And f(x) is neither even nor odd.

2)

f(x) = x³ - 3x

f(- x) = (- x³) - 3(- x)

f(- x) = - x³ + 3x

Note: The first one term in f(x) changed signs when x was replaced with (-x),

but the (constant) term did not . So the resulting f(-x) is not equal to f(x) or -f(x). And f(x) is neither even nor odd.

3)

f(x) = - x² - x⁴

f(- x) = - (- x²) - (- x⁴)

f(- x) = - x² - x⁴ = f(x)

So f(x) is Even.