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