• 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.
And now it’s time for..
The Lame Joke of the day..
What do you get when you cross Bambi with a
When do cannibals cook their victims?
On FRY - Day
3.6 A Summary of Curve
So far, you have studied several concepts that
are useful in analyzing the graph of a function.
• x-intercepts and y-intercepts
• Domain and Range
• Vertical Asymptotes
• Relative Extrema
• Points of Inflection
• Horizontal Asymptotes
1. Polynomial functions are continuous
No breaks , no holes, or gaps
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.
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.
Leading coefficient test
Tells us what is happening at the ends of the graph
(left and right behavior)
Extrema and Inflection Points
• Each polynomial of degree, n, has at most
n-1 relative extrema
And n – 2 points of inflection