Is a horizontal line an increasing or decreasing function?This is the definition of an increasing...

asigurato7

asigurato7

Answered

2022-07-19

Is a horizontal line an increasing or decreasing function?
This is the definition of an increasing and decreasing function.
"A function f(x) increases on an interval I if f ( b ) f ( a ) b > a, where a , b I. If f ( b ) > f ( a ) b > a, the function is said to be strictly increasing.
Conversely, A function f(x) decreases on an interval I if f ( b ) f ( a ) b > a, where a , b I. If f ( b ) < f ( a ) b > a, the function is said to be strictly decreasing.
Then how would a horizontal line be described? If f ( x 2 ) = f ( x 1 ) x 2 > x 1 does that mean that a horizontal line meets the definition of an increasing function and a decreasing function?

Answer & Explanation

Reese King

Reese King

Expert

2022-07-20Added 13 answers

Explanation:
Yes, an horizontal line is a function f such that f ( x ) = c for all x R , and, if a b f ( a ) = c c = f ( b ). Idem for .
Nash Frank

Nash Frank

Expert

2022-07-21Added 10 answers

Step 1
Inject f ( x ) = c in the definitions:
"A function c increases on an interval I if c c b > a, where a , b I. If c > c b > a, the function is said to be strictly increasing.
Step 2
Conversely, A function c decreases on an interval I if c c b > a, where a , b I. If c < c b > a, the function is said to be strictly decreasing."
You should be able to see for yourself what property holds.

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