Introduction to End Behavior
Object: To observe the functional values of a polynomial as the value of the independent variable increases and decreases without bound.
Exercises
1. Look at the graph of the polynomial ._ If you use the Graphing Calculator software program, does it look like the graph below?
We are not interested in specific values of the function, we are only interested in what happens when we take functional values of really big positive numbers or really big negative numbers._
- Right now, what do you think will happen to the values of f(x) when taking larger positive x values, or keep moving to the right on this graph?
- Also, right now, what do you think will happen to the values of f(x) when taking larger negative x values, or keep moving to the left on this graph?
- Let’s make sure that our guess is true._ Use the zoom out feature of the graphing software._ Does your Graphing Calculator picture look like this?
- Does this picture confirm your guesses from earlier?_ If it does not, what is your new guess?
- Use the zoom out feature again._ Does that new picture still confirm your guesses or has it changed again?
- Try the zoom out feature repeatedly._ Has your guessed been confirmed in your mind?
- Fill in the blanks with your conjecture.
- As the x values increases forever (keeps going to the right), then the y values _________________
- As the negative x values decreases forever (keeps going to the right), then the y values __________________