For each of the functions given below state the end behavior

For each of the functions given below, state the end behavior. In other words, state whether the graph rises or fall on the left, and whether the graph rises or falls on the right.

a) f(x)=4x^4 6x^5 +7x1

b) f(x)=2x^3 6x^2 +7x1

c) f(x) = (x^2 +3)(2x+4)(x5)

d) f(x) = 3x(2x + 4)(x 5)^2

Solution

a) f(x)=4x^4 6x^5 +7x1

The degree of the function is odd x^5 and the leading coefficient is -ve. So, the end behavior is:

ax x---> infinity ;f(x) ---> -infinity

as x---> -infinity ; f(x) ----> infinity

graph rises on left and falls on right

b) f(x)=2x^3 6x^2 +7x1

The degree of the function is odd x^3 and the leading coefficient is +ve. So, the end behavior is:

ax x---> infinity ;f(x) ---> infinity

as x---> -infinity ; f(x) ----> - infinity

so, graph falls on left and rises on left

c) f(x) = (x^2 +3)(2x+4)(x5)

= -2x^4........

The degree of the function is eve x^4 and the leading coefficient is -ve. So, the end behavior is:

ax x---> infinity ;f(x) ---> -infinity

as x---> -infinity ; f(x) ---->- infinity

So graph falls on both left and right

d) f(x) = 3x(2x + 4)(x 5)^2

= 6x^4.........

The degree of the function is even x^4 and the leading coefficient is +ve. So, the end behavior is:

ax x---> infinity ;f(x) ---> infinity

as x---> -infinity ; f(x) ----> infinity

Graph rises on both left and right side