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Algebra 2 > Radical Functions and Rational Exponents > Flashcards

Radical Functions and Rational Exponents Flashcards

1
Q

Properties of exponents: a^0=

a≠

A

1

0

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2
Q

Properties of exponents: a^m/a^n=

A

a^m-n

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3
Q

Properties of exponents: a^-n=

A

1/a^n

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4
Q

Properties of exponents: (ab)^n=

A

a^nb^n

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5
Q

Properties of exponents: a^m X a^n=

A

a^m+n

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6
Q

Properties of exponents: (a/b)^n=

A

a^n/b^n

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7
Q

There is one real nth root of b, denoted to radical form n√b when

A

n is odd

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8
Q

There are two real nth roots of b when b is positive and

A

n is even.

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9
Q

When the n is even and b is positive, the positive root is the … and its symbol is .
The negative root is its ________, or .

A

principal root.
n√b.
opposite
-n√b.

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10
Q

When n is even and b is negative, there are

A

no real nth roots of b.

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11
Q

What is the only nth root of 0?

A

0

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12
Q

If you write the √ sign, then you add

A

±

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13
Q

If the √ sign is already written, then it is

A

only +

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14
Q

When simplifying, there are none of these types of answers:

A

No decimal answers

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15
Q

What shows how many to find (and group)?

A

Index

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16
Q

What does n√a X n√b =, according to the combining radical expressions products property?

A

n√ab

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17
Q

What does n√a / n√b =, according to the combining radical expressions quotients property?

A

n√a/b

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18
Q

What can be used to separate the index and exponent in an expression?

A

Parentheses

19
Q

What happens with the phrase, “The grass is always greener on the other side?”

A

The negative signs fall off the numbers when they move over the fraction.

20
Q

What is the phrase that goes with the negative signs falling off when they mover over the fraction?

A

“The grass is always greener on the other side.”

21
Q

If there is an even index, what does the answer receive?

A

±

22
Q

Imaginary numbers (i) only show up in what types of problems?

A

Problems with square roots.

23
Q

If the exponent is greater than 5…

A

It’s not worth writing the long answer.

24
Q

If the exponent is greater than 5, it’s not worth writing the long answer unless

A

the base is small.

25
Q

Radical expressions can only be added and subtracted if

A

the radicands are the same.

26
Q

What still needs to be multiplied when adding and subtracting radical expressions?

A

Coefficients

27
Q

In the number k^10/7, the 10 represents the

A

exponent

28
Q

In the number k^10/7, the 7 represents the

A

index

29
Q

If the exponent is greater than 1, the answer will be

A

bigger.

30
Q

If the exponent is less than 1, the answer will be

A

smaller.

31
Q

What can sometimes be done to add and subtract radicals?

A

Simplify the radicals so that they match.

32
Q

What do you have to take when squaring a side of radical equation.

A

You have to take the whole binomial to square it.

33
Q

What are the two ways compositions can be written?

A

f ⃘ g or f(g(x))

34
Q

To find a composition, what happens to the function listed second or inside?

A

The second or inside function is used as the input into the first function. Then simplify.

35
Q

What are the four obvious ways to combine the existing functions?

A

Addition, multiplication, subtraction, division

36
Q

How is the inverse of a function found?

A

Reverse the order of the numbers in the ordered pairs (flipping the domain and range).

37
Q

What do you use to determine if your inverse is a function?

A

Horizontal line test

38
Q

What quadrant does y= √x mostly stay in?

A

The first quadrant (upper right, unless it is negative).

39
Q

What is the domain of y= √x?

A

x ≥ 0

40
Q

What is the range of y= √x?

A

y ≥ 0

41
Q

What is the domain of y= -√x?

A

x ≥ 0

42
Q

What is the range of y= -√x?

A

y ≤ 0

43
Q

What are the domain and range of y= ∛x?

A

Always all real numbers.

Algebra 2 (9 decks)

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