Lecture 4

Question 1

what is the maximum amount of turns a polynomial can have?

Answer 1

the same at the leading degree number

Question 2

how do you create for instance a cubic function from a graph?

Answer 2

1. identify the roots
2. write the roots as factors in the created equation
3. use a point to find the value the the leading coefficient

Question 3

what is the general form of a power function and what do the variables mean?

Answer 3

y=ax^(b)
b is a power
a is the leading coefficient

Question 4

what is a rational function?

Answer 4

the ratio of two polynomials

Question 5

what are the roots in the denominator of a rational function called?

Answer 5

the verticle asymtotes

Question 6

how do you find the horizontal asymptotes of a rational function?

Answer 6

use the horizontal degree rules

Question 7

what does it mean if the degree in the numerator is greater than the degree in the denominator?

Answer 7

there is no horizontal asymtote

Question 8

what does it mean if the degree in the numerator is less than the degree in the denominator?

Answer 8

the horizontal asymptote is y=0

Question 9

how do you find the x-intercepts of a polynomial function?

Answer 9

set the original function equal to zero and solve for x

Question 10

what does it mean if the degree in the numerator is the same as the degree in the denominator?

Answer 10

divide the coefficients of the terms with the same degree

Question 11

how do you find the behaviour around verticle asymptotes?

Answer 11

1. make a number line with the verticle asymptote number
2. 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

Question 12

how do you find the y-intercept of a function?

Answer 12

set x equal to zero and solve for y