Graph stuff

Question 1

vertical asymptote

Answer 1

A vertical asymptote occurs when the denominator = 0, because the function becomes undefined.

Question 2

to find x intercept
to find y intercept

Answer 2

• set y = 0
• set x = 0

Question 3

what is a function

Answer 3

a mapping such that every element of the domain is mapped to exactly one element of the range

ONE TO ONE

Question 4

a function can be

Answer 4

one to one or many to one

Question 5

rules for finding horizontal asymptote

Answer 5

✅ Rule 1: Degree of numerator < degree of denominator
Then:

y=0isthehorizontalasymptote
Example:

✅ Rule 2: Degrees are equal (numerator and denominator have same highest power)
Then:
y=
leadingcoefficientofdenominator
leadingcoefficientofnumerator

✅ Rule 3: Degree of numerator > degree of denominator
Then:

There is no horizontal asymptote

Question 6

describe the cosec graph

Answer 6

• asymptote at x = -pi, x = 0, and pi
• positive parabola, with bounds at x = -3pi/2 , pi/2 and 3pi/2

Question 7

describe the sec graph

Answer 7

asymptote at x = -pi/2 , pi/2 and -3/2 pi
parabolas with roots at : x = -pi, pi and 0