
Concept explainers
To describe : The right hand and left hand behaviour of the graph of the given function.

Explanation of Solution
Given: The function is h(x)=1−x6
According to the leading coefficient test, as x moves without bound to the left or to the right, the graph of the polynomial function f(x)=anxn+...+a1+a0 rises or falls in the following manner.
When n is odd, and the leading coefficient is positive, the graph falls to the left and rises to the right and if the leading coefficient is negative then the graph rises to the left and falls to the right.
When n is even then if the leading coefficient is positive the graph rises to the left and right and if the leading coefficient is negative then the graph falls to the left and right.
Now consider the function.
h(x)=1−x6
It can re written as,
h(x)=−x6+1
The degree of the function is even and the leading coefficient is negative. So, the graph of the function falls on both left and right hand sides.
Therefore, the graph of the function falls on both left and right hand side.
Chapter 2 Solutions
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