Polynomial Functions 3.2 Flashcards
How do you calculate the number of zeros on a graph?
Count how many times the graph crosses through the x axis
What may cause polynomials to have similar characteristics?
If they have the same degree
What indicates the end behaviours?
The degree of the leading coefficient
What are ends behaviours?
These are the observations from the graph as it goes to positive or negative infinity
How does the graph look if the leading coefficient is negative for odd degree functions?
line either straight or curvy starting from the second quadrant up and then down to the fourth quadrant
This is a x goes to negative infinity, y goes to positive infinity, and as x goes to positive infinity, y goes to negative infinity
How does the graph look if the leading coefficient is positive for odd degree functions?
line either straight of curvy starting down from the third quadrant than going up to the fourth quadrant
This is as x goes to negative infinity y goes to negative infinity, and as x goes to positive infinity, y goes to positive infinity
How does the graph look like for a negative leading coefficient for even degree functions?
Concave down
hitting second, third of fourth quadrants
This is as x goes to positive or negative infinity, y goes to negative infinity
Has same end behaviours
How does the graph look if the leading coefficient is positive for even degree functions?
Concave up
Extending mainly from the second quadrant to the first quadrant, can hit the fourth quadrant
How does the number of turning points work?
n=degree
n-1
What is the even functions test?
f(x)=f(-x)
Symetrucak across the y axis
What is the odd functions test?
f(-x)=-f(x)
Rotational symmetry about the origin
How do you tell if a graph is neither?
Has no relationship between f(x)=f(-x)
Has no symmetrical properties
