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# 3.6 -curve sketching-c

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### 3.6 -curve sketching-c

1. 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. 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. 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. 4. Pre-Calc Review 1. Polynomial functions are continuous No breaks , no holes, or gaps
5. 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. 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. 7. Leading coefficient test Tells us what is happening at the ends of the graph (left and right behavior)
8. 8. Extrema and Inflection Points • Each polynomial of degree, n, has at most n-1 relative extrema And n – 2 points of inflection
9. 9. Sketch the graph by hand f ( x) 3x 4 4x 3
10. 10. Ex 2 x2 3 3 x f (x) • Draw a graph of showing all significant features
11. 11. Closure • Find all the important values of the following function, and then graph it f (x) x 3 9x 1