# constant functions

• Jul 1st 2011, 06:38 AM
Bashyboy
constant functions
Hello, I am currently studying a section in my math book entitled "Increasing and Decreasing Functions," but my inconvience dwells in my contention with what the author states about a constant function.

Here is a picture of the figure they give me in the book

2011-07-01_10-12-23_898.jpg picture by Bashyboy - Photobucket

The rule, in the book, states that "a function f is constant on an interval if, for any Xsub1 and Xsub2 in the interval, f(Xsub1)=f(Xsub2).

So, when I try to apply this rule to our figure, I run in to the fact that segment of the constant part of the function begins at (0,1) and ends at (2,1). I know definitively that 0 does not equal 2, so I am able to deduce that I am obviously wrong in my understanding of this rule. I appreciate any whom try to answer.
• Jul 1st 2011, 06:57 AM
Plato
Re: constant functions
Quote:

Originally Posted by Bashyboy
The rule, in the book, states that "a function f is constant on an interval if, for any Xsub1 and Xsub2 in the interval, f(Xsub1)=f(Xsub2).
So, when I try to apply this rule to our figure, I run in to the fact that segment of the constant part of the function begins at (0,1) and ends at (2,1). I know definitively that 0 does not equal 2, so I am able to deduce that I am obviously wrong in my understanding of this rule.

The rule simply states that in terms of ordered pairs, every pair has the same second term for any x in the interval.
The graph is the set $\{(x,c):x\in(a,b)\}$.
• Jul 1st 2011, 08:46 AM
masters
Re: constant functions
Quote:

Originally Posted by Bashyboy
Hello, I am currently studying a section in my math book entitled "Increasing and Decreasing Functions," but my inconvience dwells in my contention with what the author states about a constant function.

Here is a picture of the figure they give me in the book

2011-07-01_10-12-23_898.jpg picture by Bashyboy - Photobucket

The rule, in the book, states that "a function f is constant on an interval if, for any Xsub1 and Xsub2 in the interval, f(Xsub1)=f(Xsub2).

So, when I try to apply this rule to our figure, I run in to the fact that segment of the constant part of the function begins at (0,1) and ends at (2,1). I know definitively that 0 does not equal 2, so I am able to deduce that I am obviously wrong in my understanding of this rule. I appreciate any whom try to answer.

Hi Bashyboy,

A constant function is f(x)=C, where C is a constant.

Your function decreases until x = 0. f(0) = 1.

Your function is constant on the interval [0, 2].

For every x in the interval [0, 2], f(x) = 1.

An application of the rule would be:

$\text{Given: }x_1=0 \text{ and } x_2=2 , f(0)=f(2)=1$