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Asymptotes, prep for limit thinking, look at graphs (IBL Calculus) 

Explore what happens when you divide a number by smaller and smaller numbers. What does this look like in a graph?

Explore what happens if you divide a number by larger and larger numbers. What does this look like in a graph?

Extension: Explore what happens to  (1-e^x)/x if x becomes smaller and smaller

Using desmos explore the roots of rational functions (in factored form). Do you notice any patterns?

Using desmos, explore what kind of shapes the graph of a rational function could be? Do you notice any patterns?

Using desmos explore the graph of the hyperbola y=1/x. Explore what changes when you put different linear terms in the numerator or denominator. What happens if the denominator is a factored quadratic equation?

Exponent rules --  by Math 355 Students at Westfield State University

Rational Exponent Exploration --  by Joey Grabowski at Westfield State University

Exponent Rule Puzzle: Can you solve it? -- by Karin Vorwerk, WSU