Question

Determine algebraically whether the function is even, odd, or neither even nor odd.

f(x) = -3x4 - 2x - 5

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

got it?

Answer 5

alright

Answer 6

yeah i get it. so its even?

Answer 7

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

Answer 8

neither. because 4 even 1s odd

Answer 9

right,

Answer 10

so this polynomial is neither

Answer 11

great!

Answer 12

thanks, can you help me with a few more?

Answer 13

sure

Answer 14

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

Answer 15

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

Answer 16

true i meant even lol
so that an even function

Answer 17

yes

Answer 18

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

Answer 19

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

Answer 20

remember, i said constants have x^0 so 7 is actually 7x^0

0 is not odd

Answer 21

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

Answer 22

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

Answer 23

both

Answer 24

both are odd?

Answer 25

yes

one has exponents 7, 5, 3 <--all are odd

the other is 5,3 ,1 <--all are odd

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

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

Answer 30

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

Answer 31

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

Answer 32

i think answers from @helder_edwin will be more precise

Answer 33

alright

Answer 34

@helder_edwin ?

Answer 35

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

Answer 36

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

Answer 37

fire away.

Answer 38

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

Answer 39

i got Increasing x > 0; Decreasing x < 0

Answer 40

no. it is increasing over the entire real line

Answer 41

always read a graph from left to right.

Answer 42

Increasing on all real numbers?

Answer 43

yes.

Answer 44

thank you!

Answer 45

u r welcome

Answer 46

@lgbasallote thanks for the referral.