In which direction does the right side of this graph point?
f(x) = 3x^3 - x^2 + 4x - 2

Question

In which direction does the right side of this graph point?
f(x) = 3x^3 - x^2 + 4x - 2

anonymous · Answer

end behavior is determined by the highest order term.  in this case, it's the x^3 term.  if it's positive, then the graph will tend toward infinity (positive direction).  if it's negative, then the graph will tend toward -infinity (negative direction).  i hope this helps.

anonymous · Answer

so negative direction?

anonymous · Answer

@binarymimic

mathstudent55 · Answer

As x gets larger approaching infinity, what happens to x^3?

ganeshie8 · Answer

why not just look at the graph and see what direction the right side is going ? https://www.desmos.com/calculator/wkjhqfp3mx

anonymous · Answer

after you answer @mathstudent55 , then pay attention to the coefficient of the x^3 term.  is it positive or negative?  i.e., does 3x^3 approach +infinity or -infinity as x gets larger and larger

anonymous · Answer

positive?

anonymous · Answer

Plot attached.

ganeshie8 · Answer

`up, down` are the directions you need to choose from

anonymous · Answer

up

ganeshie8 · Answer

yup! the graph is clearly shooting UP as you walk right on the x axis

ganeshie8 · Answer

if you go through the replies above again a couple of times, im sure you would understand how the leading term is related to the end behavior

anonymous · Answer

so the direction would ust be up. ok thanks guys for the help!