3) f(x) = -2x2(x - 2)3(x + 4)4(x - 5)
To find the degree: x2 has degree 2
(x - 2)3 has degree 3
(x + 4)4 has degree 4
(x - 5) has degree 1
adding the degrees together, we get degree 10
To find the end behavior:
right-end: put a large positive number in for each variable
-4: negative
x2 is positive
(x - 2)3 is positive
(x + 4)4 is positive
(x - 5) is positive
multiplying these together: negative ---> right-end goes downward
left-end:
put a large negative number in for each variable
-4: negative
x2 is positive
(x - 2)3 is negative
(x + 4)4 is positive
(x - 5) is negative
multiplying these together: negative ---> left-end goes downward
Zeros: bounces if the exponent is positive; passes through if the exponent is negative
x2 : bounces at 0
(x - 2)3 : passes through at 2
(x + 4)4 : bounces at -4
(x - 5) : passes through at 5
4) f(x) = 3x7 - 48x5
= 3x5(x2 - 16)
= 3x5(x + 4)(x - 4)
and now do the same type of analysis as done in problem 3).