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Section 2 - Graphs of Functions

Page history last edited by PBworks 14 years ago

 

1.2 Graphs of Functions

 

- In this section, we will be dealing with graphs of functions and trying to find the domain and range of various types of graphs.

- We will also be learning how to find the increasing, decreasing, and constant of graphs.

- In addition, we will learn how to find the maximum and minimum of graphs along with learning how to decipher between an even graph and an odd graph.

 

 

Finding the domain and range of a graph:

Domain: [-1,4) --> You get this by looking at the beginning and ends of the graph.

Range: -3,3 --> You can find this by looking at the range of the y values on the graph. This means looking at where the line begins on the y-axis and where the line ends on the y-axis.

Example: Find the domain and range of f(x)= eq=sqrt{x-4}

Domain: x-4 > 0 ---> add 4 to both sides = x>4 so... the domain is [4, §)

Range: Ask yourself... "What kind of values can f(x) be?" (there can be no negatives)

***Plug into calculator and look at the graph. Answer would be = [0,)

 

 

Determing Increasing, Decreasing, and Constant of a graph:

 

  • These are descriptions of y-values of a function.

 

Example:

Looking at the graph, you can tell the y-axis is increasing, or going up in the positive sector. In this case, the answer would be:

Inceasing (-, )

 

 

Example: Find the Increasing, Decreasing, and Constant of this function.

 

 

 

By looking at the graph, you can follow the curves of the line in order to get your increasing and decreasing.

The first section starts negative and goes up towards positive (increasing).

It stops at the point (-2,2), then goes back down to negative (decreasing) and stops at the point (2, -6).

Finally, it goes back towards positive (increasing) and will keep going on for infinite.

Answer:

Increasing: (-, -2)

Decreasing: (-2, 2)

Increasing: (2, )

 

 

Finding Relative Maximums and Minimums

Graph on your calculator! 

 

 

 

Even and Odd Functions (or Neither):

Even: Symmetric to the y-axis

 

Odd: Symmetric about origin

 

Even (x,y) and (-x,y) --> plug in (-x) and get f(x)

Odd (x,y) and (-x,-y) --> plug in (-x) and get -f(x)

 

 

Example: f(x) = x² + 2 <-- Plug in (-x)

                           = (-x)² + 2

                           = x² + 2

The original function is the same as the answer, so it is an even function.

 

 

Example: f(x) = 3x³ - x <-- Plug in (-x)

                           = 3(-x)³ - (-x)

                           = -3x³ + x

The original function is the opposite of the answer, so it is an odd function.

 

 

If all of the powers in the function are even, then the function is even.

If all of the powers in the function are odd, then the function is odd.**

 

 

Comments (1)

Anonymous said

at 8:18 pm on Jan 8, 2008

Somehow the pictures need to be fixed... you're missing some good graphs from it, I think! The spacing got a little goofy near the end... and max/min was left out. 16/20

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