Determine algebraically whether the function is even, odd, or neither even nor odd.
f(x) = -3x4 - 2x - 5

- anonymous

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- schrodinger

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- lgbasallote

there's a shortcut to knowing...just look at the exponents of *every* x. What are the exponents of every x in this case?

- anonymous

4 & 1.
would i add them? and its odd?

- lgbasallote

nope. remember: any constant is rewritten as cx^0 for example, 1 can be rewritten as 1x^0
2 can be rewritten as 2x^0
so 5 is 5x^0

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## More answers

- lgbasallote

so the exponents of x are actually 4, 1 and 0
got it?

- anonymous

alright

- anonymous

yeah i get it. so its even?

- lgbasallote

now, look at 4, 1, 0 <--are these numbers even, odd or neither?

- anonymous

neither. because 4 even 1s odd

- lgbasallote

right,

- lgbasallote

so this polynomial is neither

- anonymous

great!

- anonymous

thanks, can you help me with a few more?

- lgbasallote

sure

- anonymous

before that, can you give me an example of an odd function?
would that be like f(x) = -5x^6 - 4x^4 - 7x^2 ?

- lgbasallote

the exponents in this case are 6, 4 and 2..are those numbers odd?

- anonymous

true i meant even lol
so that an even function

- lgbasallote

yes

- anonymous

f(x) = -5x^5 - 4x^3 - 7
woul that be odd?

- anonymous

it would be except for the 7, which ruins it
the degree of a constant is 0, and 0 is an even number

- lgbasallote

remember, i said constants have x^0 so 7 is actually 7x^0
0 is not odd

- anonymous

so f(x) = -5x^5 - 4x^3 - 7x ?

- anonymous

or f(x) = -5x^7 - 4x^5 - 7x^3

- lgbasallote

both

- anonymous

both are odd?

- lgbasallote

yes
one has exponents 7, 5, 3 <--all are odd
the other is 5,3 ,1 <--all are odd

- anonymous

okay. so the next question.
Use the graph of f to estimate the local maximum and local minimum

- anonymous

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- lgbasallote

don't you just look at the "turning points" of that graph?

- anonymous

i thought so, but last tiem i got it wrong so i want to double check.

- anonymous

Local maximum: approx. (-1,1.17); local minimum: approx. (2,-3.33) ?

- lgbasallote

hmm...i'm not a master of graphs so i'm afraid i'll have to ask help from @helder_edwin

- anonymous

alright. theres one more. its graphs too tough. but i have choices, maybe that will help?

- lgbasallote

i think answers from @helder_edwin will be more precise

- anonymous

alright

- anonymous

@helder_edwin ?

- helder_edwin

u r right. u got a local maximum at x=-1 and a local minimun at x=2.

- anonymous

alright. i have one more. can you let me know if im correct?

- helder_edwin

fire away.

- anonymous

Determine the intervals on which the function is increasing, decreasing, and constant

- anonymous

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- anonymous

i got Increasing x > 0; Decreasing x < 0

- helder_edwin

no. it is increasing over the entire real line

- helder_edwin

always read a graph from left to right.

- anonymous

Increasing on all real numbers?

- helder_edwin

yes.

- anonymous

thank you!

- helder_edwin

u r welcome

- helder_edwin

@lgbasallote thanks for the referral.

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