6.1-5 Quiz

Question 1

Sum of a Function

Answer 1

(f+g)(x)=f(x)+g(x)

Question 2

Difference of a Function

Answer 2

(f-g)(x)=f(x)-g(x)

Question 3

Product of a Function

Answer 3

(fg)(x)=f(x)g(x)

Question 4

Quotient of a Function

Answer 4

(f/g)(x)=f(x)/g(x); such that g(x)=/0

Question 5

Compositions of Functions

Answer 5

Another method to combine functions
(fog)(x)=f(g(x))

Question 6

Perfect Squares

Answer 6

1, 4, 9, 16, 25, 36, 49, 64, 81, 100

Question 7

Perfect Cubes

Answer 7

1, 8, 27, 64, 125, 216, 343, 512, 729, 1000

Question 8

Perfect Fourths

Answer 8

1, 16, 81, 256, 625, 1296, 2401, 4096, 6561, 10000

Question 9

The nth Root of a Real Number, a, Can Be Written As

Answer 9

n√a

Question 10

Index

Answer 10

n
Number outside of radical
If there is no index, it is assumed that n=2

Question 11

Radical

Answer 11

√

Question 12

Radicand

Answer 12

a
Number inside radical

Question 13

Even Roots

Answer 13

Positive and negative

Question 14

Odd Roots

Answer 14

Pay attention to signs
Only one

Question 15

Even Index Positive Radicand

Answer 15

Two real roots

Question 16

Odd Index Positive Radicand

Answer 16

One real root

Question 17

Odd Index Negative Radicand

Answer 17

One real root

Question 18

Even Index Negative Radicand

Answer 18

Two imaginary roots

Question 19

If A Radicand Has More Than One Root

Answer 19

The radical sign indicates only the principal root

Question 20

Principal

Answer 20

Positive

Question 21

Square Roots

Answer 21

Exponents must be multiples of two

Question 22

Cube Roots

Answer 22

Exponents must be multiples of three

Question 23

Fourth Roots

Answer 23

Exponents must be multiples of four

Question 24

Steps to Adding and Subtracting Radicals

Answer 24

1. Simplify all radicals
2. Identify radicals with the same index and same radicand as only these can be combined
3. For common radicals, add/subtract the coefficients and keep the common radical

Question 25

Steps to Multiplying Radicals

Answer 25

1. Multiply coefficients then use the product rule
2. Simplify the resulting radical

Question 26

Product Rule

Answer 26

n√an√b=n√ab

Question 27

Steps to Dividing Radicals

Answer 27

1. Divide coefficients then use the quotient rule
2. Simplify the resulting radical

Question 28

Quotient Rule

Answer 28

n√a/n√b=n√a/b

Question 29

Monomial Denominators

Answer 29

Multiply the numerator and denominator by the radical

Question 30

Binomial Denominators

Answer 30

Multiply the numerator and denominator by the conjugate

Question 31

Conjugate

Answer 31

Same expression but opposite sign in the middle

Question 32

a^1/n

Answer 32

The nth root of a
n√a

Question 33

a^m/n

Answer 33

The nth root of a, raised to the mth power
n√a^m or (n√a)^m

Question 34

Steps to Simplifying Expressions with Radical Exponents

Answer 34

1. Rewrite all radicals in exponential form
2. Use the exponent rules to simplify the expression
3. Write your answer as a radical in the simplest form, rationalize if needed

Question 35

Radical Number

Answer 35

Must be bigger to take out