Question

1-Using the words: odd; even; or neither, classify each of the following functions.U must provide supporting evidence for your classification?
1- f(x) - 2x + 1
2- f(x) 4x^2 - 3
3- f(x) 3x^3 - 2x^2 + 5
4- f(x) 1/x^3 -5x

Answer 1

for a function to be even f(x) = f(-x)
for an odd function f(-x) = - f(x)

Answer 2

so for Number 2
f(1) = 4(1)^2 -3 = 4 -3 = 1
f(-1) = 4(-1)^2 - 3 = 4 - 3 = 1

so this is an even function

Answer 3

even functions are symmetrical about the y-axis

Answer 4

What about the answer of 3 and 4
can you also help in it plz

Answer 5

and odd functions have got origin symmetry

Answer 6

find f(1) and f(-1) for number 3
what do you get?

Answer 7

3(1)^3 - 2((1)^2 + 5 = ?
3(-1)^3 - 2((-1)^2 + 5 = ?

Answer 8

if it does ot fit the requirements for even and odd then it is neither

Answer 9

3(1)^3 - 2((1)^2 + 5
= 3 - 2 + 5 = 6
3(-1)^3 - 2((-1)^2 + 5 = -3 -2 + 5 = 0

Answer 10

- so that is neither

Answer 11

sorry gotta go right now

Answer 12

and what abut fourth one ?

Answer 13

thnak you for your help i ll try 4th by my self you are genius :)

Answer 14

thanks

Answer 15

it's the same process as welsh said

for a function to be even f(x) = f(-x)
for an odd function f(-x) = - f(x)

to see whether f(x) = 1/x^3 -5x is even or odd, we can use two steps:

1. to test whether f(x) is even, evaluate f(1) and f(-1). if they are the same, then the function is even. otherwise, the function is not even.
2. to test whether f(x) is odd, evaluate f(-1) and -f(1), if they are the same, then the function is odd. otherwise, the function is not odd

Answer 16

so can you help in 4th one ?