DOMAIN AND RANGE DOMAIN – LIST OF ALL X VALUES RANGE – LIST OF ALL Y VALUES ONE WAY YOU OFTEN SEE THIS ON THE IB: INTERVAL NOTATION WRITE THE BEGINNING AND ENDING VALUES OF THE INTERVAL [ OR ] IMPLIES THAT THE VALUE IS INCLUDED IN THE INTERVAL ( OR ) IMPLIES THAT THE VALUE IS NOT INCLUDED INFINITY IS ALWAYS WRITTEN WITH A ROUND BRACKET
TEST YOUR UNDERSTANDING WRITTEN IN INTERVAL NOTATION
TO THE NEXT LEVEL Assume f(x) = 5x-2 Assume g(x) = x-10 What do you think f(g(x)) is? What do you thing g(f(x)) is? I challenge you to find an instance where f(g(x)) = g(f(x)) What do you think g(f(3)) is? How would you solve that? What about f(g(-2))?
The graph of a function and it’s inverse are symmetrical about the line y=x
INVERSE FUNCTIONS AND COMPOSITES One way to determine if two functions are inverses of one another is to use composite functions. It is known that: This is one way to check if you correctly found the inverse of a function. This is also one way to determine if two seemingly unrelated functions are inverses of one another. Try a few simple examples on your own!
SIGN DIAGRAMS A quick representation of the graph’s behavior. Will come in handy as we begin to study calculus next year. Can help with trying to figure out the appearance of a graph of a complicated function.