1.1 & 1.2 - Function's Graphs and Mathematical Reading

On Friday, we learned about how to read mathematical writing, such as that in our textbook, and about the graphs of functions.

Function Review: A function is a mathematical relation that assigns each input exactly one output. A function can be detected by the vertical line test, in which a vertical line is drawn along the graph in order to ensure that each x-value (input) has only one y-value (output). It is also important to remember that f(x)=y. 

Graphing of a Function: Although each function graph must pass the vertical line test in order to be a function, there are different kinds of function graphs. 

A function is increasing on an interval if, for any  and  in the interval, < implies .

A function is decreasing on an interval if, for any  and  in the interval, < implies .

A function is called a constant of  if there exists an interval (,) that, for any  and  in the interval, .

A function value  is called a relative maximum of  if there exists an interval (,) that contains  such that  implies .

A function value  is called a relative minimum of  if there exists an interval (,) that contains  such that  implies .

A function  is an even function if, for each  in the domain of , .

QUICK TIP: Even functions are symmetric to the y-axis.

A function  is an odd function if, for each  in the domain of , .

QUICK TIP: Odd functions are symmetric to the origin.

QUICK QUIZ:

See if you can tell what kind of function each of these graphs are:

1.

 

2.

 

3.

 

ANSWERS:

1. This graph is neither even or odd because it is not symmetrical to the y-axis or the origin, but has a relative maximum around (-0.7, 1.4) and a relative minimum around (0.6, 0.6).

2. This graph is an odd function because it is symmetric to the origin.

3. This graph is an even function because it is symmetric to the y-axis.