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- 1. Warm up • Compile a list of any concepts that are useful in sketching a graph by hand. • Think of anything we have done this year, as well as previous years of math.
- 2. And now it’s time for.. The Lame Joke of the day.. What do you get when you cross Bambi with a ghost? Bamboo When do cannibals cook their victims? On FRY - Day
- 3. 3.6 A Summary of Curve Sketching So far, you have studied several concepts that are useful in analyzing the graph of a function. • x-intercepts and y-intercepts (P.1) • Symmetry (P.1) • Domain and Range (P.3) • Continuity (1.4) • Vertical Asymptotes (1.5) • Differentiability (2.1) • Relative Extrema (3.1) • Concavity (3.4) • Points of Inflection (3.4) • Horizontal Asymptotes (3.5)
- 4. Pre-Calc Review 1. Polynomial functions are continuous No breaks , no holes, or gaps
- 5. Zeros of polynomials • Zeros are the same as x-intercepts. • Zeros happen when f(x) = 0 Zero = solution = factor If x = c is a zero of polynomial, then x – c is a factor of the polynomial.
- 6. The Fundamental Theorem of Algebra • Every polynomial of degree, n, has exactly n roots. • Repeated roots: – An even number of repeats will touch the x-axis. – An odd number of repeats will cross the x-axis.
- 7. Leading coefficient test Tells us what is happening at the ends of the graph (left and right behavior)
- 8. Extrema and Inflection Points • Each polynomial of degree, n, has at most n-1 relative extrema And n – 2 points of inflection
- 9. Sketch the graph by hand f ( x) 3x 4 4x 3
- 10. Ex 2 x2 3 3 x f (x) • Draw a graph of showing all significant features
- 11. Closure • Find all the important values of the following function, and then graph it f (x) x 3 9x 1

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