Rational Functions

Question 1

Rationals: How can you find: holes

Answer 1

y= a (x-r)/ c(x-r)
same factor in the numerator and denominator

Question 2

Rationals: How can you find: y-intercept

Answer 2

y=b/d

Question 3

Rationals: How can you find: vertical asymptote

Answer 3

x= -d/c
at the zeroes of the denominator (not a hole)

Question 4

Rationals: How can you find: zero

Answer 4

x= -b/a

Question 5

Rationals: How can you find: horizontal asymptote

Answer 5

y= a/c

Question 6

what is the base rational function?

Answer 6

f(x) = ax + b / cx + d

Question 7

What do you have to make sure to do to every rational function first?

Answer 7

Factor if possible!!! (even common factoring)

Question 8

What is the reciprocal of: 2x-3

Answer 8

1/ 2x-3

Question 9

What is the reciprocal of: 3x +6

Answer 9

1/ 3x+6

Question 10

Explain the factored form process

Answer 10

common factor, SPF, put it all together! (might have to use quadratic formula)

Question 11

Explain the vertex form process

Answer 11

common factor first two terms, (b/2)^2, add and subtract that in brackets, take subtracted term and multiply it out of brackets using number from common factor, SPF in brackets

Question 12

Where are the vertical asymptotes for a reciprocal function?

Answer 12

At the zeroes of the base function

Question 13

What are the horizontal asymptotes for a reciprocal function?

Answer 13

y=0

Question 14

For the positive and negative intervals of a function does the reciprocal have the same intervals?

Answer 14

Yes, they are the same

Question 15

For intervals of increase and decrease in a function does the reciprocal have the same intervals?

Answer 15

No, it is opposite

Question 16

Where are the points of intersection for a reciprocal function and its base?

Answer 16

at (x,1) and (x,-1)

Question 17

What is the vertex reciprocal?

Answer 17

(h, 1/k)

Question 18

what is a reciprocal function?

Answer 18

the output of the original function is flipped