What is the end behavior?

Question

-x⁴-x³-2x²+x-3

Answer 1

Hilton is correct.  Look at the equation itself...

As x gets larger at either end the largest term will

be the highest exponent... -x⁴  so that is the term

which will drive the main direction in which the

graph goes.

 

Since the exponent '4' is even then x⁴ will always

be positive regardless of whether x is positive or negative.

 

Because the coefficient of the highest term x⁴ is negative,

then the -x⁴ will always be a negative number and

the output  will get larger and larger

in the negative direction on both ends of the graph.

 

Thus the output of the function f(x) = -x⁴-x³-2x²+x-3

will go down towards -∞ as x →∞ on either end.

Answer 2

f(x) = -x4-x3-2x2+x-3

 

Since this is a quartic function  with a = -1, both the left and the right ends of the graph descend to negative infinity.