Even and Odd Functions


In Exercises 47–62, say whether the function is even, odd, or neither. Give reasons for your answer.


g(x) = x/(x² − 1)

Theory and Examples

The variables r and s are inversely proportional, and r = 6 when s = 4. Determine s when r = 10.

Even and Odd Functions

In Exercises 47–62, say whether the function is even, odd, or neither. Give reasons for your answer.

sin x²

Even and Odd Functions

In Exercises 47–62, say whether the function is even, odd, or neither. Give reasons for your answer.

h(t) = |t³|

Even and Odd Functions

In Exercises 47–62, say whether the function is even, odd, or neither. Give reasons for your answer.

g(x) = x⁴ + 3x² − 1

Even and Odd Functions

In Exercises 47–62, say whether the function is even, odd, or neither. Give reasons for your answer.

f(x) = x² + x

Increasing and Decreasing Functions

Graph the functions in Exercises 37–46. What symmetries, if any, do the graphs have? Specify the intervals over which the function is increasing and the intervals where it is decreasing.

y = −x³

The Greatest and Least Integer Functions

Does ⌊x⌋ = ⌈x⌉ for all real x? Give reasons for your answer.