Which of the following polynomials could have the same end behavior as f(x)=ax^6+bx^5+c?

There may be more than one correct answer. Select all correct answers.

a. nx^5+bx^4+c

b. kx+b

c. dx^4−bx^3−cx^2+dx+e

d. −jx^8+bx^7+cx^4

e. −mx^2

can someone help me with this it is confusing and there is more than one answer so yea i need help

3 answers

ax^6 has a range that tends towards positive infinity.
Any function that has a +2, 4,6,8 as the power, and has a leading numerical coefficient that is POSITIVE has a range that tends towards positive infinity...
Does that help ??
it sort of makes sense could you explain it a little further
If the power is EVEN the ends of the graph go upwards towards the sky! Both arms of the function go upwards.
that is 2x^2, 4^6, 1x^8 etc all have leading coefficients that are positive so the graphs go upwards.
if the function was y = - x^2 then the graph would go downwards (in quadrants 3 and 4).
You may wish to use www.desmos to graph your functions so you can see what I am describing : )
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