http://www.ck12.org Chapter 1. Functions and Graphs
A interval is said to bestrictlyincreasing iff(b)<f(c)is substituted into the definition.
Decreasingmeans places on the graph where the slope is negative. The formal definition of decreasing and strictly
decreasing are identical to the definition of increasing with the inequality sign reversed.
A function is calledmonotonicif the function only goes in one direction and never switches between increasing and
decreasing.
Identifying analytically where functions are increasing and decreasing often requires Calculus. For PreCalculus, it
will be sufficient to be able to identify intervals graphically and through your knowledge of what the parent functions
look like.
Example A
Identify which of the basic functions are monotonically increasing.
Solution:Of the basic functions, the monotonically increasing functions are:
f(x) =x,f(x) =x^3 ,f(x) =āx,f(x) =ex,f(x) =lnx,f(x) = 1 +^1 eāx
The only basic functions that are not monotonically increasing are:
f(x) =x^2 ,f(x) =|x|,f(x) =^1 x,f(x) =sinx
Example B
Identify whether the green, red or blue function is monotonically increasing and explain why.