Rational Expressions Flashcards
Rational numbers can be written as _________.
fractions
5x-7 / 3x^2 is an example of a ________ __________.
rational expression
If there is no GCF, what is the next step?
Factor the top and bottom of the expression.
After factoring the top and bottom of the expression, cancel ________ factors on the ___ and ______.
matching
top
bottom
If we don’t know what the value of _ is, we are ____.
n
done
Steps of solving rational expression: simplify then multiply.
Step 1
Steps of solving rational expression: factor as much as possible.
Step 2
Steps of solving rational expression: cancel matches on the top and bottom.
Step 3
Steps of solving rational expression: multiply what is left.
Step 4
In final answers, there are no ________ exponents.
negative
In order to add and subtract fractions, what do two fractions need to do?
Share a common denominator.
What is the first phase of simplifying a complex fraction?
Make the top into 1 fraction.
What is the second phase of simplifying a complex fraction?
Make the bottom into 1 fraction.
What is the third phase of simplifying a complex fraction?
Top / bottom
What is the main plan for solving rational equations?
Make the denominators the same on both sides of the equal sign.
When all of the denominators are the same, what can you do?
Cross them out; they don’t matter anymore.
Why can you not add to make the denominators the same? What must you do instead?
It changes the value of the fraction. You must multiply or divide.
When it is a quadratic equation, what must you do to solve it?
Have a zero on one side to solve.
Once solutions have been found, what must you do?
Check for extraneous solutions.
What number can’t be used to divide by?
0
What is the math theory for crossing out the matching denominators out?
The problem has been multiplied to get rid of the denominators on both sides.
F(x) = 1/x is a _________.
Hyperbola
A hyperbola consists of 2 symmetrical ________.
branches
The domain and range of a hyperbola are
all nonzero numbers.
Why is zero not the domain or range of a hyperbola?
0 can’t be a denominator.
Any function of the form g(x) = a/x (a≠0) has the same _________, domain, and range as the function f(x) = 1/x
asymptote
What is an asymptote of a hyperbola?
Lines that a hyperbola approaches but doesn’t intersect.
Asymptotes tell where the graph ____ ___ __.
does not go
Domain and range tell where the graph ____ __.
does go
What does x-h tell in y=(a/x-h)+k?
Vertical asymptote
What does k tell in y=(a/x-h)+k?
Horizontal asymptote
To find the y-intercept plug in =.
x=0
To find the x-intercept plug in =.
y=0
What does a negative rational function do to the graph?
Flips it.
What does a negative rational function do to the asymptotes?
Nothing.
Horizontal asymptotes: top wins.
No horizontal asymptote.
Horizontal asymptotes: bottom wins.
Y=0
Horizontal asymptotes: tie.
Y=coefficients.
