Rational Expressions

Question 1

Rational numbers can be written as _________.

Answer 1

fractions

Question 2

5x-7 / 3x^2 is an example of a ________ __________.

Answer 2

rational expression

Question 3

If there is no GCF, what is the next step?

Answer 3

Factor the top and bottom of the expression.

Question 4

After factoring the top and bottom of the expression, cancel ________ factors on the ___ and ______.

Answer 4

matching
top
bottom

Question 5

If we don’t know what the value of _ is, we are ____.

Answer 5

n

done

Question 6

Steps of solving rational expression: simplify then multiply.

Answer 6

Step 1

Question 7

Steps of solving rational expression: factor as much as possible.

Answer 7

Step 2

Question 8

Steps of solving rational expression: cancel matches on the top and bottom.

Answer 8

Step 3

Question 9

Steps of solving rational expression: multiply what is left.

Answer 9

Step 4

Question 10

In final answers, there are no ________ exponents.

Answer 10

negative

Question 11

In order to add and subtract fractions, what do two fractions need to do?

Answer 11

Share a common denominator.

Question 12

What is the first phase of simplifying a complex fraction?

Answer 12

Make the top into 1 fraction.

Question 13

What is the second phase of simplifying a complex fraction?

Answer 13

Make the bottom into 1 fraction.

Question 14

What is the third phase of simplifying a complex fraction?

Answer 14

Top / bottom

Question 15

What is the main plan for solving rational equations?

Answer 15

Make the denominators the same on both sides of the equal sign.

Question 16

When all of the denominators are the same, what can you do?

Answer 16

Cross them out; they don’t matter anymore.

Question 17

Why can you not add to make the denominators the same? What must you do instead?

Answer 17

It changes the value of the fraction. You must multiply or divide.

Question 18

When it is a quadratic equation, what must you do to solve it?

Answer 18

Have a zero on one side to solve.

Question 19

Once solutions have been found, what must you do?

Answer 19

Check for extraneous solutions.

Question 20

What number can’t be used to divide by?

Answer 20

0

Question 21

What is the math theory for crossing out the matching denominators out?

Answer 21

The problem has been multiplied to get rid of the denominators on both sides.

Question 22

F(x) = 1/x is a _________.

Answer 22

Hyperbola

Question 23

A hyperbola consists of 2 symmetrical ________.

Answer 23

branches

Question 24

The domain and range of a hyperbola are

Answer 24

all nonzero numbers.

Question 25

Why is zero not the domain or range of a hyperbola?

Answer 25

0 can’t be a denominator.

Question 26

Any function of the form g(x) = a/x (a≠0) has the same _________, domain, and range as the function f(x) = 1/x

Answer 26

asymptote

Question 27

What is an asymptote of a hyperbola?

Answer 27

Lines that a hyperbola approaches but doesn’t intersect.

Question 28

Asymptotes tell where the graph ____ ___ __.

Answer 28

does not go

Question 29

Domain and range tell where the graph ____ __.

Answer 29

does go

Question 30

What does x-h tell in y=(a/x-h)+k?

Answer 30

Vertical asymptote

Question 31

What does k tell in y=(a/x-h)+k?

Answer 31

Horizontal asymptote

Question 32

To find the y-intercept plug in =.

Answer 32

x=0

Question 33

To find the x-intercept plug in =.

Answer 33

y=0

Question 34

What does a negative rational function do to the graph?

Answer 34

Flips it.

Question 35

What does a negative rational function do to the asymptotes?

Answer 35

Nothing.

Question 36

Horizontal asymptotes: top wins.

Answer 36

No horizontal asymptote.

Question 37

Horizontal asymptotes: bottom wins.

Answer 37

Y=0

Question 38

Horizontal asymptotes: tie.

Answer 38

Y=coefficients.