Chapter Sections 3.3-3.5 Flashcards
Which part of the rational function is the domain
The bottom part of the “fraction”
What does a rational function look like?
R(x)=p(x)/q(x)
What do you use to solve for the x and y intercepts
Use the top part of the “fraction”
Where do the verticals and holes come from?
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
What does end behavior look like for graphs like 1/x or rational functions
As x -> neg. infinity, f(x) -> whatever your HORIZONTAL ASYMPTOTE IS
As x -> pos. infinity, f(x) -> whatever your HORIZONTAL ASYMPTOTE IS
What does intermediate behavior look like for 1/x or rational functions?
As x -> VA - (from left), f(x) -> pos. or neg. infinity
As x -> VA + (from right), f(x) -> pos. or neg. infinity
What happens to a graph like this (meaning transformations)
F(x)=(1/x-2) +1
The horizontal asymptote moves up to 1
What happens if the graph is f(x)= (1/x^2)
The is an “L” in the first quadrant and a backwards “L” in the second quadrant.
What happens to a graph like this f(x)= (1/(x+1)^2) +1
The is an “L” in the first quadrant and a backwards “L” in the second quadrant. And The horizontal asymptote moves up to 1
What is the horizontal asymptote if the top part of the fraction has a smaller exponent than the bottom.
HA: y=0
What is the horizontal asymptote if the top part of the fraction has an equal exponent than the bottom.
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
What is the horizontal asymptote if the top part of the fraction has a bigger exponent than the bottom.
There is no horizontal asymptote
When do you try to find an oblique or other?
When the top portion of the rational function has a bigger exponent than the bottom.
What would an oblique asymptote look like?
Y=mx+b
What would an “other” asymptote look
Like?
Y= Ax^n
Ex y=4x^2
When finding out if a rational function is even (meaning -f(x)) what should you make sure of?
To distribute the negative sign to ALL parts of the top portion of the rational function
REMEMBER
plot holes if there are any
What do you do if you have f(x)= (a/c)+(b/d) and want to simplify?
(ad+bc)/cd
How do you find out if something is factorable?
Put equation in discriminant formula. If it is a perfect square then it can be factored
How do you solve polynomial inequalities? For example x^2-9<0
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)
How do you know if you should include the boundaries in inequality’s interval?
If in the inequality it only says < or > then don’t include.
How or what does it mean when it asks to support graphically.
Draw the graph of the polynomial. Then draw a squiggly line in between the intervals. That is the interval.
REMEMBER
Put open or closed dots on graph according to what the inequality says.
What happens when a polynomial has NO SOLUTION
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.
What do you do if you have a rational inequality?
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.
What is the equation for inverse variation?
Y=k/x
What is the equation for joint variation?
Z=kxy
