Question

Determine the end behavior of the given polynomial function:

Answer 1

Hardest question!!!!

Answer 2

not at all
what is the degree of the polynomial? that is pretty much all you need to know, that, and the leading coefficient

Answer 3

(even or odd)

Answer 4

so postive then negative

Answer 5

? did you find the degree?

Answer 6

The function can be re-written as\[(x^2 -9)(x^3-5)^2\] when x tends to - infinity the exponents (just plug a very very negative value for x to check ) would make the substituted value positive so the function would tend to +infinity. Similarly when x tens to + infinity (plug a very large positive value for x)then the function again tends to +infinity. SO both ends of the function point upwards.

Answer 7

infinity?

Answer 8

the number line goes to infinity on both ends

Answer 9

I'll show you, just a sec

Answer 10

when we say + infinity we mean a very very very large positive number

Answer 11

similarly when say -infinity we mean a very very very very negative number something like -1000000000000000000000000000000000000000000000000000000000000000000

Answer 12

but my answers don have nummbers

Answer 13

the term infinity basically means that if you can think of a very very very large number infinity is still larger.

Answer 14

we don't deal with actual numbers here, just the idea of very very very large numbers

Answer 15

the function will have a graph , right?

Answer 16

and the graph goes on beyond the size of a page?

Answer 17

we don't actually see the "ends" just the limits of our sketch

Answer 18

for example

Answer 19

the shape is called the parabola, but the ends that you see on the picture are not the actual ends of the function, just the point where we stopped drawing the curve

Answer 20

when we talk of the end behavior we mean to say that the check if the ends point upwards towards the + side of the Y axis or downwards towards the negative side of the Y axis

Answer 21

are you following?

Answer 22

yes but its hard

Answer 23

which grade are you in? I'll tell it you in the relevant terms.

Answer 24

11th

Answer 25

then you must have worked with quadratic equations?

Answer 26

so the end infinity sign must be negative right?

Answer 27

plotting graphs from tabular values like