Explain why functions with the property f(–x) = –f(x) are called odd functions and functions with the property f(–x) = f(x) are called even functions.

The functions with the property f(–x) =f(x) are called even functions because they symmetric about the y-axis and The functions with the property f(–x) = -f(x) are called odd because these function are symmetric about the origin .

Step-by-step explanation:

The functions with the property f(–x) =f(x) are called even functions because they symmetric about the y-axis . In other words these functions usually take a form x^2 ,x^4 ,x^6 ,x^8 etc . However ,there are other functions that behave like that too, such as cos(x).An even exponent does not always make an even function, for example (x+1)^2 is not an even function .

The functions with the property f(–x) = -f(x) are called odd because these function are symmetric about the origin . In other words they are called odd because of the functions like x, x^3 ,x^5 ,x^7, etc .but there are other functions that behave like that, too, such sin(x) .but an odd exponent does not always make an odd function, for example x3+1 is not an odd function.

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.

a

explanation: