0. Functions

Given the graph of the following function, determine the intervals on which $f\left(x\right)$  is increasing.

Given the graph of the following function, determine the intervals on which $f\left(x\right)$  is decreasing.

Given the graph of the following function, determine where the graph reaches a maximum.

Analyzing slopes Use the points A, B, C, D, and E in the following graphs to answer these questions. <IMAGE>

a. At which points is the slope of the curve negative?

State whether each function is increasing, decreasing, or neither.

c. Height above Earth’s sea level as a function of atmospheric pressure (assumed nonzero)

State whether each function is increasing, decreasing, or neither.

d. Kinetic energy as a function of a particle’s velocity

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

a. ƒ(x) = |x - 2| + 1

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

d. R(x) = √ 2x - 1

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

𝔂 = e⁻ˣ²

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|