Question

Describe the end behavior of polynomial graphs with odd and even degrees. Talk about positive and negative leading coefficients.

Answer 1

think of the "end behaviour" of a line with positive or negative slope

Answer 2

I just started this and my teacher told me to try this tonight and I don't understand it at all

Answer 3

if the slope of a line is positive then as \(x\to \infty\) you have \(y\to \infty\) also

Answer 4

and as \(x\to -\infty\) also \(y\to -\infty\) this is true of any odd polynomial with positive leading coefficient

Answer 5

still very confused

Answer 6

@satellite73

Answer 7

Those are the notes my teacher gave me.

Answer 8

If a number has an even exponent, both sides of the graph are going to have the same end behaviour: either they will both go towards \[\infty\] or -\[\infty\]

Answer 9

\[-\infty \]

Answer 10

so is that the answer?

Answer 11

If the number has an even exponent and a positive coefficient, that means both sides of the graph are going to head towards positive infinity.
x→-∞ then y→∞ and x→∞ then y→∞

Answer 12

Just for positive even exponent haha

Answer 13

if the number has a negative coefficient and an even exponent then instead it will be
x→-∞ then y→-∞ and x→∞ then y→-∞

Answer 14

Like in those two graphs ^^

Answer 15

Now if a number has an odd exponent, one side of the graph will go towards negative infinity and one side will go towards positive infinity

Answer 16

If its a negative coefficient and odd exponent, it'll look like this:

Answer 17

so first it heads towards positive infinity and then negative infinity.
x→-∞ then y→∞ and x→∞ then y→-∞

Answer 18

but if its an odd exponent and positive coefficient, it would be
x→-∞ then y→-∞ and x→∞ then y→∞

Answer 19

Sooo
2x^4 x→-∞ then y→∞ and x→∞ then y→∞
-2x^4 x→-∞ then y→-∞ and x→∞ then y→-∞
2x^3 x→-∞ then y→-∞ and x→∞ then y→∞
-2x^3 x→-∞ then y→∞ and x→∞ then y→-∞

Answer 20

@thenikko so it would be positive goes up and negative goes down?

Answer 21

For even exponents

Answer 22

@thenikko so what would the answer be? For positive exponents positive goes up and negative goes down. But with an odd exponent the both go towards positive?

Answer 23

For positive, even exponents both go up.
For negative, even exponents both go down.
For positive, odd exponents it goes down and then up.
For negative, odd exponents it goes up and then down