Rational Expressions Flashcards

1
Q

Rational numbers can be written as _________.

A

fractions

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2
Q

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

A

rational expression

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3
Q

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

A

Factor the top and bottom of the expression.

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4
Q

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

A

matching
top
bottom

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5
Q

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

A

n

done

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6
Q

Steps of solving rational expression: simplify then multiply.

A

Step 1

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7
Q

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

A

Step 2

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8
Q

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

A

Step 3

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9
Q

Steps of solving rational expression: multiply what is left.

A

Step 4

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10
Q

In final answers, there are no ________ exponents.

A

negative

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11
Q

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

A

Share a common denominator.

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12
Q

What is the first phase of simplifying a complex fraction?

A

Make the top into 1 fraction.

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13
Q

What is the second phase of simplifying a complex fraction?

A

Make the bottom into 1 fraction.

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14
Q

What is the third phase of simplifying a complex fraction?

A

Top / bottom

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15
Q

What is the main plan for solving rational equations?

A

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

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16
Q

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

A

Cross them out; they don’t matter anymore.

17
Q

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

A

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

18
Q

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

A

Have a zero on one side to solve.

19
Q

Once solutions have been found, what must you do?

A

Check for extraneous solutions.

20
Q

What number can’t be used to divide by?

A

0

21
Q

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

A

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

22
Q

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

A

Hyperbola

23
Q

A hyperbola consists of 2 symmetrical ________.

A

branches

24
Q

The domain and range of a hyperbola are

A

all nonzero numbers.

25
Q

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

A

0 can’t be a denominator.

26
Q

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

A

asymptote

27
Q

What is an asymptote of a hyperbola?

A

Lines that a hyperbola approaches but doesn’t intersect.

28
Q

Asymptotes tell where the graph ____ ___ __.

A

does not go

29
Q

Domain and range tell where the graph ____ __.

A

does go

30
Q

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

A

Vertical asymptote

31
Q

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

A

Horizontal asymptote

32
Q

To find the y-intercept plug in =.

A

x=0

33
Q

To find the x-intercept plug in =.

A

y=0

34
Q

What does a negative rational function do to the graph?

A

Flips it.

35
Q

What does a negative rational function do to the asymptotes?

A

Nothing.

36
Q

Horizontal asymptotes: top wins.

A

No horizontal asymptote.

37
Q

Horizontal asymptotes: bottom wins.

A

Y=0

38
Q

Horizontal asymptotes: tie.

A

Y=coefficients.