Question

Which of the following describes the end behavior of the graph of the function

f(x) = –2x^5 – x^3 + x – 5

A.Downward to the left and upward to the right

B.Upward to the left and downward to the right

C.Downward to the left and downward to the right

D.Upward to the left and upward to the right

Answer 1

get a "feel" for the numbers.

for large values of x, isn't the first term "hugely negative" ?

for large negative values of x, isn't the first term 'hugely positive' ?

so where does the graph tend to go ?

Answer 2

Aren't both terms negative? I was going to say the answer was

B. Upward to the left and downward to the right

but you make it sound like

A.Downward to the left and upward to the right

Answer 3

no,
read my reply again

try x = 10 and x = -10 (values which arent' even "large")

the term that dominates is -2x^5
for x=10, x^5 = 100000
and -2x^5 = -200000

if x=-10, -2x^5 = =2(-100000) = +200000

so what does the graph do?

You are right, it goes upward to the left and downward to the right, as I also suggested in my first reply.