Jill, let's talk about graphs and their restrictions. Here is an equation on the board.
Cool, where do we begin?
If you were to plug this into your calculator, this is what would appear. What do you notice?
I notice that it doesn't move that far to the left.
Good job Jill, what you are noticing is called a restriction.
What is a restriction?
It means that the variable cannot have the value of the numbers being restricted
How do I know what the restriction in this equation is?
Well in logarithms, when X is in that position, it has to be greater than 0 because 10^X can not equal zero. Basically any number to any power will never equal zero.
Well our equation is different, what is the restriction for Y=(log(x-3))?
Basically you have to figure out what numbers for X that X-3 won't be less than or equal to zero. Those are the numbers greater than 3. Therefore, all numbers less than or equal to 3 are restricted. Then you would draw that dotted line on the graph to show the restriction.
Wow, thanks! I'm glad I know now that some graphs have restrictions! Thanks, Bob!