Flashcards in Rational Expressions Deck (38)

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1

## Rational numbers can be written as _________.

### fractions

2

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

### rational expression

3

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

### Factor the top and bottom of the expression.

4

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

###
matching

top

bottom

5

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

###
n

done

6

## Steps of solving rational expression: simplify then multiply.

### Step 1

7

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

### Step 2

8

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

### Step 3

9

## Steps of solving rational expression: multiply what is left.

### Step 4

10

## In final answers, there are no ________ exponents.

### negative

11

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

### Share a common denominator.

12

## What is the first phase of simplifying a complex fraction?

### Make the top into 1 fraction.

13

## What is the second phase of simplifying a complex fraction?

### Make the bottom into 1 fraction.

14

## What is the third phase of simplifying a complex fraction?

### Top / bottom

15

## What is the main plan for solving rational equations?

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

16

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

### Cross them out; they don't matter anymore.

17

## 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.

18

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

### Have a zero on one side to solve.

19

## Once solutions have been found, what must you do?

### Check for extraneous solutions.

20

## What number can't be used to divide by?

### 0

21

## 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.

22

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

### Hyperbola

23

## A hyperbola consists of 2 symmetrical ________.

### branches

24

## The domain and range of a hyperbola are

### all nonzero numbers.

25

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

### 0 can't be a denominator.

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

### asymptote

27

## What is an asymptote of a hyperbola?

### Lines that a hyperbola approaches but doesn't intersect.

28

## Asymptotes tell where the graph ____ ___ __.

### does not go

29

## Domain and range tell where the graph ____ __.

### does go

30

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

### Vertical asymptote

31

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

### Horizontal asymptote

32

## To find the y-intercept plug in _=_.

### x=0

33

## To find the x-intercept plug in _=_.

### y=0

34

## What does a negative rational function do to the graph?

### Flips it.

35

## What does a negative rational function do to the asymptotes?

### Nothing.

36

## Horizontal asymptotes: top wins.

### No horizontal asymptote.

37

## Horizontal asymptotes: bottom wins.

### Y=0

38