AP Calculus WHY YES … BECAUSE … YOU’RE IN... Mandatory Graphs OH NO … WORK ALREADY??? What he say? Come again... Lot’s of hard work Lot’s of FUN!!!

AP Calculus

… Is there a ceiling?? … Is there a floor??? What happens to y as x  or x  -  … or as x  c...

Or as we say in the business: “CONCAVITY” Concave UpConcave Down

1. Observe the graph State the equation Practice for reflex...

Domain: (- ,  ) Range:[0, )) Decreases ‘til x = 0, then Increases Constant UPWARD curvature... i.e. CONCAVE UP on (- ,  ) Minimum at (0, 0)...No upper bound There is a better way to state this... Decreasing on (- , 0] & Increasing on [0,  )

Domain: (- ,  ) Range:(- ,),) Increases for all x … (  x)... (- ,  ) DOWNWARD CONCAVITY: (- ,0) UPWARD CONCAVITY: (0,  ) No lower bound...No upper bound

TRANSFORMATIONS VERTICAL SHIFTS HORIZONTAL SHIFTS VERTICAL STRETCHES

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1

Asymptotes

RATIONAL FUNCTIONS

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1 Asymptotic

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Also known as...

Allow me to introduce you To a few of my other friends!

The Greatest Integer of x