Chapter Sections 3.3-3.5

Question 0

Which part of the rational function is the domain

Answer 0

The bottom part of the “fraction”

Question 1

What does a rational function look like?

Answer 1

R(x)=p(x)/q(x)

Question 2

What do you use to solve for the x and y intercepts

Answer 2

Use the top part of the “fraction”

Question 3

Where do the verticals and holes come from?

Answer 3

VA are from the bottom and usually the same as the domain UNLESS there are holes. Holes are factors that are cancelled on both bottom and top of the “fraction”. These do not become VA’s

Question 4

What does end behavior look like for graphs like 1/x or rational functions

Answer 4

As x -> neg. infinity, f(x) -> whatever your HORIZONTAL ASYMPTOTE IS

As x -> pos. infinity, f(x) -> whatever your HORIZONTAL ASYMPTOTE IS

Question 5

What does intermediate behavior look like for 1/x or rational functions?

Answer 5

As x -> VA - (from left), f(x) -> pos. or neg. infinity

As x -> VA + (from right), f(x) -> pos. or neg. infinity

Question 6

What happens to a graph like this (meaning transformations)

F(x)=(1/x-2) +1

Answer 6

The horizontal asymptote moves up to 1

Question 7

What happens if the graph is f(x)= (1/x^2)

Answer 7

The is an “L” in the first quadrant and a backwards “L” in the second quadrant.

Question 8

What happens to a graph like this f(x)= (1/(x+1)^2) +1

Answer 8

The is an “L” in the first quadrant and a backwards “L” in the second quadrant. And The horizontal asymptote moves up to 1

Question 9

What is the horizontal asymptote if the top part of the fraction has a smaller exponent than the bottom.

Answer 9

HA: y=0

Question 10

What is the horizontal asymptote if the top part of the fraction has an equal exponent than the bottom.

Answer 10

HA: y= a/b
Meaning that the horizontal asymptote is made up of the exponents from the whole rational function. For example (5x-1)/(3x+1) ….HA: y=5/3

Question 11

What is the horizontal asymptote if the top part of the fraction has a bigger exponent than the bottom.

Answer 11

There is no horizontal asymptote

Question 12

When do you try to find an oblique or other?

Answer 12

When the top portion of the rational function has a bigger exponent than the bottom.

Question 13

What would an oblique asymptote look like?

Answer 13

Y=mx+b

Question 14

What would an “other” asymptote look

Like?

Answer 14

Y= Ax^n

Ex y=4x^2

Question 15

When finding out if a rational function is even (meaning -f(x)) what should you make sure of?

Answer 15

To distribute the negative sign to ALL parts of the top portion of the rational function

Question 16

REMEMBER

Answer 16

plot holes if there are any

Question 17

What do you do if you have f(x)= (a/c)+(b/d) and want to simplify?

Answer 17

(ad+bc)/cd

Question 18

How do you find out if something is factorable?

Answer 18

Put equation in discriminant formula. If it is a perfect square then it can be factored

Question 19

How do you solve polynomial inequalities? For example x^2-9<0

Answer 19

Split up the x^2-9 into (x+3)(x-3) then from there you get the boundaries 3 and -3. Test a number before -3, in between -3 and 3, and a number after 3. Find if they are negative or positive. Do the number line thing. Whatever goes along with inequality is the answer or interval. In this question whatever is negative in the “number line” is the answer. So (-3,3)

Question 20

How do you know if you should include the boundaries in inequality’s interval?

Answer 20

If in the inequality it only says < or > then don’t include.

Question 21

How or what does it mean when it asks to support graphically.

Answer 21

Draw the graph of the polynomial. Then draw a squiggly line in between the intervals. That is the interval.

Question 22

REMEMBER

Answer 22

Put open or closed dots on graph according to what the inequality says.

Question 23

What happens when a polynomial has NO SOLUTION

Answer 23

When this happens test ANYTHING! If it’s true then it’s all real numbers or (negative infinitive to positive infinity) if it’s false then no solution.

Question 24

What do you do if you have a rational inequality?

Answer 24

You find the boundaries which are the answers to x on the top and bottom of the “fraction”. There can be more than 2 boundaries. Then test numbers that are either less than, in between, more than the boundaries. Do the number line thing. Then which ever agree with the inequality sign are the answers. Be aware that some numbers might not be included in intervals and will have a () because they are VA.

Question 25

What is the equation for inverse variation?

Answer 25

Y=k/x

Question 26

What is the equation for joint variation?

Answer 26

Z=kxy