Question

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

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

(note: the 3x4 is an exponent as in 3x to the 4th power)

Answer 1

^4 is the usual ascii notation for an exponent

Answer 2

but good clarification nonetheless

Answer 3

ah my bad

Answer 4

if f(-1) = f(1), its even

if f(-1) = - f(1), its odd

otherwise its neither

Answer 5

for example, x^2 is an even function

(-1)^2 = (1)^2 .. its even




x^3 is an odd function

(-1)^3 = - (1)^3

Answer 6

so.. this would be an odd function?

Answer 7

let test it out ...

f( 1) = -3 - 2 - 5 = -10
f(-1) = -3 + 2 - 5 = -6



is f(-1) = f(1) ? -6 = -10
is f(-1) = - f(1) ? -6 = 10

of neither, then neither

Answer 8

So its neither? jesus im so confused XD where did the -10 and -6 come from

Answer 9

when x = -1, f(-1) = -10 its just working the function, replace x by -1 and add up the terms :/

Answer 10

if we try this algebrically, we would use a more generic input like x = -a, and x=a

Answer 11

the -1 and 1 are just simpler values to "see" with

Answer 12

f( a) = -3a^4 - 2a - 5
f(-a) = -3a^4 + 2a - 5


-3a^4 - 2a - 5 ?=? -3a^4 + 2a - 5

-3a^4 - 2a ?=? -3a^4 + 2a

- 2a ?=? 2a

-a ?=? a; only if a = 0

Answer 13

okay so the answer to the problem would be neither, correct? i just need an answer at this point im terrible with functions, i get the concept, its just applying it in pre calculus is an issue for me.

Answer 14

neither, yes

Answer 15

thanks :D

Answer 16

http://www.wolframalpha.com/input/?i=y+%3D++-3x4+-+2x+-+5

visually, if the graph is a mirror image across the y axis, its even

if its a rotation thru the origin by 180 degrees, its odd