Question

@hartnn Two Olympic swimmers, Ryan and Michael, create unique ripple waves in the water. The function created by Ryan is f(x) = 4x2 + 7. The function created by Michael is f(x) = 4x2 - 5x + 3. Describe to Ryan and Michael, using complete sentences, which of the operations—addition, subtraction, multiplication, and division—will result in the largest degree function and which operation will result in the smallest degree function.

Answer 1

do you know what 'degree of a function' means ?

Answer 2

yes sir :)

Answer 3

then do you know what operation can increase the degree?

Answer 4

use an operation for both functions.. for example add f(x) = 4x^2 + 7 and f(x) = 4x^2- 5x + 3 ?

Answer 5

thats what it means ?

Answer 6

what is the degree of 'x^2' ?
what is the degree of 'x^3' ?

what is x^2 * x^3 ??

what is the degree of the above result ?

Answer 7

6

Answer 8

sure?
x^2 * x^3 = x^{2+3} = .. ?

Answer 9

oh right cuz u add em cx so 5

Answer 10

yes, so can we conclude
multiplying polynomial increases the degree? :)

Answer 11

yes

Answer 12

so if multiplication increases,
what operation will decrease the degree?

Answer 13

subtraction o-o ?

Answer 14

no...what is the opposite operation of multiplication ?

Answer 15

division

Answer 16

yes.
though in some cases (like this), subtraction will also result in reduction of degree :)

Answer 17

how would i do it with these functions ?

Answer 18

what i mean is use multiplication and division with these functions given

Answer 19

you need to do all those 4 operations.

check the result.
and based on that, prove that
multiplication will increase the degree
subtraction and division will reduce the degree
and addition will have no effect on degree

Answer 20

but how do i do that.. 4x^2 * 4x^2 * x^1 ? or how

Answer 21

you can only describe by giving this example
\(Multiplication : x^2 \times x^2 = x^4 \)
degree is maximum
\(Subtraction : x^2 -x^2 = 0 \)
degree is minimum

Answer 22

ok ...

Answer 23

x^2 + x^2 = x^4 ?

Answer 24

x^2+ x^2 = 2x^2
same degree

Answer 25

x^2 / x^2 = x ?

Answer 26

x^2/x^2 = 1
degree = 0

Answer 27

wait but subtraction and division both r = to 0 degree ?

Answer 28

yes,
division always reduces the degree
but subtraction reduces sometimes only...
when the co-efficient of the highest degree term is same

Answer 29

in this case.. it reduced in both.. so which is least ?

Answer 30

in this particular example, both gives you the least :)
you can go with subtraction, because it is easy to calculate :)