Question

Two Martians, Splott and Fizzle, invite you to pilot their giant robot. The heat generated by one leg mechanism is represented by the function f(x) = 3x2 + 20. The heat generated by one arm mechanism is represented by g(x) = 3x2 + 4x - 5. Describe to Splott and Fizzle, using complete sentences, which operation results in the largest degree function and which operation results in the smallest degree function. Show your work to justify your reasoning.

Answer 1

Do every operation
find the one that gives the highest degree
Explain that to Splott and Fizzle
Then tell them to leave so you can do "real math"

Answer 2

So you just solve for x and figure which x is bigger?

Answer 3

No you don't solve for x. Just find the operation with the highest and smallest degree

Answer 4

How do I do that? That's why I was asking because I don't know how to do that.

Answer 5

Oh
Do you know all the basic mathematical operations you can do with polynomial functions?

Answer 6

yes

Answer 7

I don't know how to find the degree.

Answer 8

See that exponent over the first x in f(x). That is the degree of the function. Simply because it is the biggest exponent.

Answer 9

When comparing two functions in this case, you're comparing the degrees and trying to find which is bigger.

Answer 10

So in this are the degrees the same?

Answer 11

Yes

Answer 12

How about we walk through all the operations to find the highest degree?

Answer 13

ok

Answer 14

Alright
Let h(x) be the result of any operation between f(x) and g(x)
What is h(x) when you do f(x) + g(x)?
What is the degree of h(x)?

Answer 15

2?

Answer 16

Good
What is the degree when you subtract the two functions?

Answer 17

1?

Answer 18

And what about division?

Answer 19

1?

Answer 20

Not sure, we'll have to actually do it. Either 1 or 0.
How about multiplication though?

Answer 21

4?

Answer 22

What is the operation that gives you the highest degree?

Answer 23

Multiplication

Answer 24

Last the lowest ones would be addition, subtraction and division

Answer 25

I think it is only division

Answer 26

when you divide them you get -4/4x so wouldn't that still be 1?

Answer 27

Actually you're right sorry. but it's not addition. Just subtraction and division

Answer 28

ok thank you :)

Answer 29

No problem :)
Make sure you show your work for each operation.
Good job
AND remember to explain to Fizzle :P