Graphs of Functions 1.2

A graph of a function is the collection of coordinate points (x, f(x)), and that:

x is the distance from the y-axis, while f(x) is the distance from the x-axis

The first thing that is important in graphing a function is finding its domain and range

For example:

But in order to find the domain and range of this function, we can not have a negative inside the radical, so the problem must be changed to an inequality in which it would look like this:

0 < -2x+3

Then you would add 2x to both sides, now the expression would look like 2x < 3

To finish the problem and find the domain, divide by 2 on both sides, and the domain would come out to be x < 1.5

The graphical solution would look very similar to this, and because the graph is always going to have a range of equal to, or less than 0.


Increasing and Decreasing Functions

We know if a function is decreasing if,

X₁<X₂ 

implies

and if it's increasing, just switch the inequality sign around.

The function is constant when

Relative Minimum and Maximum Values

A funnction that has a relative minimum of f contains a so that f(a) < f(x)

and that a function with a relative maximum of f contains a so that f(a) > f(x)

Even and Odd Functions

Even Function

Odd Function

A function is even when the x in the domain f is f(-x) = f(x)

A function is odd when the x in the domain f is f(-x) = -f(x)

 

Hopefully this blog was helpful in learning how to graph functions, and finding domain/range.