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
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 ?
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
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.
To determine the end behavior of a function, we need to examine the highest degree term in the polynomial. In this case, the highest degree term is -2x^5.
Since the exponent of the highest degree term is odd (5 is odd), the end behavior of the graph will be opposite on the left and right sides of the graph.
When x approaches negative infinity (the left side), the coefficient of the highest degree term is negative (-2), which means the graph moves downward.
When x approaches positive infinity (the right side), the coefficient of the highest degree term is also negative (-2), which means the graph moves downward.
Therefore, the correct answer is:
C. Downward to the left and downward to the right