This is the second piece to my site about functions
With your knowledge of functions, you can tell whether it is increasing or decreasing
When the function is increasing, x and y are both increasing.
When the function is decreasing, x is increasing while y is decreasing
The increasing and decreasing of functions can be placed in a mathematic equation
Increasing: If a function y=f(x) is defined on an interval [a,b], then f(x) is increasing on [a,b], whenever x1 is less than x2, then f(x1) is less than f(x2).
Decreasing: A function is decreasing on [a,b], if, whenever x1 is less than x2, then f(x1) is greater than f(x2).
Graphs of Distance vs. Time in math can be described in these words...
The function is increasing at a faster rate
The function is increasing at a slower rate
The function has increasing function values
The function has decreasing function values
The function remains constant
The function remains at a constant rate
This is a Distance vs. Time graph
Composite Functions
A composite functions is when you put two or more functions together
You place these functions together via the x values in the equations
Composite functions can be written such as f(g(x)), or fog(x){the o in this situation stands for of}
One equation is placed into another via x, such as....
f(x)=x+3
g(x)=x+4
f(g(x))=(x+4)+3 - Where the first function's x is exchanged for the second function's equation
If a the two functions are inverses of eachother, the value of their composition should equal x
So if f(x) and g(x) are inverses of eachother, then f(g(x))=x and g(f(x))=x
A graph of a composite function with equations that are inverses of each other should mirror over the line y=x
A composite function will only truly work if the two or more equations contain the same variables
A composite function can be composed of more than two functions, such as h(f(g(r(e(x)))))
This is an image of a composite function:
This is an image of a graph of a composite function:
Quiz 2: put your knowledge of functions into use
Question 1
How do you know if a function is increasing?
The x and y values are both increasing
The x value is increasing, while the y value is decreasing
The x value is decreasing, while the y value is increasing
Question 2
What does a Distance vs. Time graph have to deal with?
Values that are never constant
Values that increase of decrease at different rates, as well as remain constant
Values that can only remain constant
Question 3
What pertains to a composite function?
A composite function is a function where one equation is placed into another via a variable
A composite function has equations that are inverses of eachother equals x
