Radical Functions and Rational Exponents Flashcards
Properties of exponents: a^0=
a≠
1
0
Properties of exponents: a^m/a^n=
a^m-n
Properties of exponents: a^-n=
1/a^n
Properties of exponents: (ab)^n=
a^nb^n
Properties of exponents: a^m X a^n=
a^m+n
Properties of exponents: (a/b)^n=
a^n/b^n
There is one real nth root of b, denoted to radical form n√b when
n is odd
There are two real nth roots of b when b is positive and
n is even.
When the n is even and b is positive, the positive root is the … and its symbol is .
The negative root is its ________, or .
principal root.
n√b.
opposite
-n√b.
When n is even and b is negative, there are
no real nth roots of b.
What is the only nth root of 0?
0
If you write the √ sign, then you add
±
If the √ sign is already written, then it is
only +
When simplifying, there are none of these types of answers:
No decimal answers
What shows how many to find (and group)?
Index
What does n√a X n√b =, according to the combining radical expressions products property?
n√ab
What does n√a / n√b =, according to the combining radical expressions quotients property?
n√a/b
What can be used to separate the index and exponent in an expression?
Parentheses
What happens with the phrase, “The grass is always greener on the other side?”
The negative signs fall off the numbers when they move over the fraction.
What is the phrase that goes with the negative signs falling off when they mover over the fraction?
“The grass is always greener on the other side.”
If there is an even index, what does the answer receive?
±
Imaginary numbers (i) only show up in what types of problems?
Problems with square roots.
If the exponent is greater than 5…
It’s not worth writing the long answer.
If the exponent is greater than 5, it’s not worth writing the long answer unless
the base is small.
Radical expressions can only be added and subtracted if
the radicands are the same.
What still needs to be multiplied when adding and subtracting radical expressions?
Coefficients
In the number k^10/7, the 10 represents the
exponent
In the number k^10/7, the 7 represents the
index
If the exponent is greater than 1, the answer will be
bigger.
If the exponent is less than 1, the answer will be
smaller.
What can sometimes be done to add and subtract radicals?
Simplify the radicals so that they match.
What do you have to take when squaring a side of radical equation.
You have to take the whole binomial to square it.
What are the two ways compositions can be written?
f ⃘ g or f(g(x))
To find a composition, what happens to the function listed second or inside?
The second or inside function is used as the input into the first function. Then simplify.
What are the four obvious ways to combine the existing functions?
Addition, multiplication, subtraction, division
How is the inverse of a function found?
Reverse the order of the numbers in the ordered pairs (flipping the domain and range).
What do you use to determine if your inverse is a function?
Horizontal line test
What quadrant does y= √x mostly stay in?
The first quadrant (upper right, unless it is negative).
What is the domain of y= √x?
x ≥ 0
What is the range of y= √x?
y ≥ 0
What is the domain of y= -√x?
x ≥ 0
What is the range of y= -√x?
y ≤ 0
What are the domain and range of y= ∛x?
Always all real numbers.
