Q. 6 - Precalculus Enhanced with Graphing Utilities

Question

Concepts and Vocabulary

A function f is ___________ on an open interval I if, for any choice of x1 and x2 in I, with  $x_1<x_2 we have f\left(x_1\right)<f\left(x_2\right)$

Step-by-Step Solution

Answer

A function f is increasing on an open interval  I if, for any choice of x1 and x2 in I, with 

$x_1<x_2 we have f\left(x_1\right)<f\left(x_2\right)$

Given information

Given that in a function f on open interval I

$x_1<x_2 we have f\left(x_1\right)<f\left(x_2\right)$

Step 2: Function

Given that ,

$$\begin{gathered} x_1 and x_{2}on I. x_1<x_2 we have f\left(x_1\right)<f\left(x_2\right) \\ When x values are increa\sin g then function values are also increa\sin g \end{gathered}$$

A function f is increasing on an open interval  I if, for any choice of x1 and x2 in I, with 

$x_1<x_2 we have f\left(x_1\right)<f\left(x_2\right)$