what is the maximum amount of turns a polynomial can have?
the same at the leading degree number
how do you create for instance a cubic function from a graph?
- identify the roots
- write the roots as factors in the created equation
- use a point to find the value the the leading coefficient
what is the general form of a power function and what do the variables mean?
y=ax^(b)
b is a power
a is the leading coefficient
what is a rational function?
the ratio of two polynomials
what are the roots in the denominator of a rational function called?
the verticle asymtotes
how do you find the horizontal asymptotes of a rational function?
use the horizontal degree rules
what does it mean if the degree in the numerator is greater than the degree in the denominator?
there is no horizontal asymtote
what does it mean if the degree in the numerator is less than the degree in the denominator?
the horizontal asymptote is y=0
how do you find the x-intercepts of a polynomial function?
set the original function equal to zero and solve for x
what does it mean if the degree in the numerator is the same as the degree in the denominator?
divide the coefficients of the terms with the same degree
how do you find the behaviour around verticle asymptotes?
- make a number line with the verticle asymptote number
- plug in numbers before and after the value of interest to see the behaviour around the asymptote
- if one side approaches a negative number, the function is going to negative infinity
– if one side approaches a positive number, the function is going to positive infinity
how do you find the y-intercept of a function?
set x equal to zero and solve for y
