0. Functions

In Exercises 9–16, determine whether the function is even, odd, or neither.

𝔂 = x⁵ - x³ - x

In Exercises 9–16, determine whether the function is even, odd, or neither.

𝔂 = sec x tan x

In Exercises 9–16, determine whether the function is even, odd, or neither.

𝔂 = x⁴ + 1

x³ - 2x

In Exercises 9–16, determine whether the function is even, odd, or neither.

𝔂 = x - sin x

In Exercises 9–16, determine whether the function is even, odd, or neither.

𝔂 = x cos x

Suppose that ƒ and g are both odd functions defined on the entire real line. Which of the following (where defined) are even? odd?

a. ƒg

b. ƒ³

c. ƒ(sin x)

d. g(sec x)

e. |g|

In Exercises 5–8, determine whether the graph of the function is symmetric about the 𝔂-axis, the origin, or neither.

𝔂 = x²/⁵

In Exercises 5–8, determine whether the graph of the function is symmetric about the 𝔂-axis, the origin, or neither.

𝔂 = x² - 2x - 1

In Exercises 9–16, determine whether the function is even, odd, or neither.

𝔂 = 1 - cos x

In Exercises 9–16, determine whether the function is even, odd, or neither.

𝔂 = x² + 1

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 = 1/|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 = x³/8

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 = (−x)²/³

Find the largest interval on which the given function is increasing.

b. ƒ(x) = (x + 1)⁴

Find the largest interval on which the given function is increasing.

c. g(x) = (3x - 1)¹/³