Question

Select the description of f(x) = –3 – x^6.

An odd function with end behavior of the graph that increases to the right and to the left.

An odd function with end behavior of the graph that decreases to the right and to the left.

An even function with end behavior of the graph that increases to the right and to the left.

An even function with end behavior of the graph that decreases to the right and to the left.

Answer 1

Odd functions, like linear ones, always continue diagonally, in a sense. Even functions are like U's or W's - both ends face either up together or down together.

By definition, positive odd functions go from the bottom left of the coordinate plane to the top right. Positive even functions have upward arrows. Opposite directions apply for negative functions, as you may assume.

Answer 2

to determine whether a graph is even or odd you look at the degree of the function
if it is odd then the function is odd, if the degree is even then the function is even

to determine whether the graph points up or down, you must first know the basic end behavior of the odd or even graph
if the graph is even and positive it points up both sides
if the graph is even and negative it points down both sides
if the graph is odd and positive the right side points up and the left side points down
if the graph is odd and negative the right side points down and the left side points up

in your case the degree is even (6 is an even degree) and the function is negative
given the info i provided above, what is the graph of a negative even function?