0. Functions

State whether the functions represented by graphs A , B , C and in the figure are even, odd, or neither. <IMAGE>

Symmetry Determine whether the graphs of the following equations and functions are symmetric about the x-axis, the y-axis, or the origin. Check your work by graphing.

$\text{ƒ}\left(x\right)=x^4+5x^2-12$

Symmetry Determine whether the graphs of the following equations and functions are symmetric about the x-axis, the y-axis, or the origin. Check your work by graphing.

$\text{ƒ}\left(x\right)=x{}^5-x^3-2$

Symmetry Determine whether the graphs of the following equations and functions are symmetric about the x-axis, the y-axis, or the origin. Check your work by graphing.

$x^{\frac{2}{3}}+y^{\frac{2}{3}}=1$

Symmetry Determine whether the graphs of the following equations and functions are symmetric about the x-axis, the y-axis, or the origin. Check your work by graphing.

$\text{ƒ}\left(x\right)=x\mid x\mid$

Identify the symmetry (if any) in the graphs of the following equations.

$y^2-4x^2=4$

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