1.7-1.11 Quiz

Question 1

(1.7) Characteristics of a rational function

Answer 1

• Has asymptotes
• MUST have a variable in the denominator

Question 2

(1.7) How do you find horizontal asymptotes?

Answer 2

by looking at the degree and leading coefficient of the top and bottom functions

Question 3

(1.7) If the top degree is less than the bottom degree, how do you find the horizontal asymptote?

Answer 3

1. If the top degree is less than the bottom degree, asymptote is y=0

Question 4

(1.7) If the degrees are the same, how do you find the horizontal asymptote?

Answer 4

2. If the degrees are the same, divide the leading coefficients to find the horizontal asymptotes

Question 5

(1.7) If the top degree is greater than the bottom degree, how do you find the horizontal asymptote?

Answer 5

3. If the top degree is greater than the bottom degree, then there is no horizontal asymptote*

*unless the top is 1 more than the horizontal asymptote, then there’s an oblique asymptotes

Question 6

(1.7) If the top degree is greater than the bottom degree, what part of the function has the same end behavior as the function?

Answer 6

the quotient of the top and bottom leading terms

Question 7

(1.7) How do you find oblique (slant) asymptotes?

Answer 7

Long division (divide the numerator by the denominator until the remainder is a constant or a variable with a smaller degree than the divisor), and the quotient (the answer WITHOUT the remainder) is the slope of the oblique asymptote

Question 8

(1.8) How do you find the zeros of a rational function?

Answer 8

1. Factor the bottom and top
2. Check for holes
3. Set each of the top terms equal to zero

Question 9

(1.9) How do you tell whether a factor is a hole or an asymptote?

Answer 9

If the factor’s degree is higher on the top, it’s a hole. If it’s the same on both, it’s a hole. If it’s higher on the bottom, it’s an asymptote.

Question 10

(1.11) What are the steps to draw a rational function?

Answer 10

First: Simplify function!!!

1. Find holes, VA, HA, and zeros
2. Find the domain (interval notation)
3. Draw a sketch (use points to figure out where the curves are)

Question 11

(1.11) What is Pascal’s Triangle?

Answer 11

A pattern that helps you figure out how to expand binomials.

Question 12

(1.11) What are the numbers in Pascal’s Triangle?

Answer 12

As shown below:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1

Question 13

(1.11) What is the pattern for Pascal’s Triangle?

Answer 13

Numbers next to each other add up (Like a factoring tree!)

Question 14

(1.11) What do the numbers in Pascal’s Triangle mean?

Answer 14

They correspond to the coefficients of each term

Question 15

(1.11) What is the degree of each term in Pascal’s triangle?

Answer 15

The leading coefficient’s degree is the degree you’re expanding it to, and it goes down by one. Same with Y, but from the other side.