use the leading coefficient test to determine the end behavi

use the leading coefficient test to determine the end behavior of the graph of the given polynomial function

f(x)= -5x^6 - 2x^4 + 2x^3 + 6

a. falls left and rises right
b. rises left and falls right 
c. falls left and falls right 
d. rises left and rises left 
e. none of the above

Solution

Remember that when degree of given function is Even then both ends of graph goes in same direction.

when degree of given function is Odd then both ends of graph goes in opposite direction.

In given function f(x)= -5x^6 - 2x^4 + 2x^3 + 6, degree is 6 which is Even so both ends of graph will be in same direction, may be up or down.

Now look at the leading coefficient (-5), which is negative.

Negative sign means graph starts from bottm on left side.

so that concludes choice C is correct.

c. falls left and falls right