For the polynomial
f(x)=2x^4-8x^2+7x-25
as
x→ - ∞, f(x)→ ∞
A. True
B. False

Question

For the polynomial
f(x)=2x^4-8x^2+7x-25
as
 x→ - ∞, f(x)→ ∞
A. True
B. False

ganeshie8 · Answer

its an even degree polynomial

ganeshie8 · Answer

remember the end behavior ?

ganeshie8 · Answer

it goes only in one direction based on leading coeffecient

ganeshie8 · Answer

since, the leading coefficient here is positive, it goes positive infinity in both ends.. 

x→ - ∞
x→ + ∞

anonymous · Answer

http://www.mathway.com/graph_image.aspx?p=f(x)=2x^4-8x^2+7x-25?p=520?p=450?p=False?p=False?p=False?p=False?p=False?p=False?p=True?p=True?p=-10?p=10?p=-50?p=10?p=4

ganeshie8 · Answer

its ok to graph... but you dont need to. you can answer these by eyeballing the equation

ganeshie8 · Answer

how  ?

ganeshie8 · Answer

see the graph, as you go extreme left of X axis, the graph is increasing more and more up right ?

anonymous · Answer

well you said 
since, the leading coefficient here is positive, it goes positive infinity in both ends.. 

x→ - ∞
x→ + ∞

and the question says 
x→ - ∞, f(x)→ ∞

so wouldnt it have to be x→ + ∞? idk im getting confused

ganeshie8 · Answer

both ends it goes +∞ means,

as x→ - ∞, f(x) → + ∞
as x→ + ∞, f(x) → + ∞

anonymous · Answer

oh ok i see now but i dont understand the first part x→ - ∞

ganeshie8 · Answer

first part is input, next part is value of function

ganeshie8 · Answer

ok lets draw the graph and see

anonymous · Answer

So its True because the leading coef. is positive?
ok

amistre64 · Answer

the equation: 2x^4-8x^2+7x-25  at sufficiently |large| values of x  gets controled by the first term

f(x) = 2x^4

ganeshie8 · Answer

yes. amistre explanation above says why leading coef alone controls the end behavior... try taking some time to ponder over it.. :)

anonymous · Answer

im getting confusedddd ahhh.... im sorry but i dont get what @amistre64 was saying ....is it saying since it has a degree of 4 it takes control over the whole equation?

amistre64 · Answer

essentially yes

amistre64 · Answer

at large value of |x|  you get

2(large)^4 + (piddly little stuff that is so small compared to the first term that they might as well be zero) ....

anonymous · Answer

ok so since it is positive it would be x→ + ∞ ?

this is what im getting really confused on..

anonymous · Answer

oh ok @amistre64