0. Functions

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.

$\text{ƒ}\left(x\right)=x^4+5x^2-12$

Which of the functions graphed in Exercises 1–6 are one-to-one, and which are not?

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

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

𝔂 = x⁴ + 1

x³ - 2x

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

b. ƒ(x) = (x + 1)⁴

Is x¹² an even or odd function? Is sin x² an even or odd function?

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

a. ƒ(x) = |x - 2| + 1

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