Thread: 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.

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 .

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: