6.1-3 Quiz Flashcards
Sums with Functions
(f+g)(x)=f(x)+g(x)
Differences with Functions
(f-g)(x)=f(x)-g(x)
Products with Functions
(fg)(x)=f(x)g(x)
Quotients with Functions
(f/g)(x)=f(x)/g(x)
Quotients with Functions Exception
g(x)≠0
Restrictions in Domain
Set x=0 and solve
Domain restriction (inf, #)U(#, inf)
Composite Function
(fog)(x)=f(g(x))
Functions When X is a Number
Substitute number
Perfect Squares
1, 4, 9, 16, 25, 36, 49, 64, 81, 100
Perfect Cubes
1, 8, 27, 64, 125, 216, 343, 512, 729, 1,000
Perfect Fourths
1, 16, 81, 256, 625, 1,296, 2,401, 4,096, 6,561, 10,000
The nth Root of a Real Number, a
Can be written as the radical expression n√a
Index
Small number above radical
Radical
√
Radicand
Number inside radical
If There is No Index
It is assumed that n=2
Even Possible Roots
Positive or negative answer
Odd Possible Roots
Pay attention to signs
Only one answer
Index Even
Radicand positive with 2 real roots
Radicand negative with 2 imaginary roots
Index Odd
Radicand positive with one real root
Radicand negative with one real root
If a Radical Has More Than One Root
The radical sign indicates only the principal, or positive, root
Exponents Must Be
Multiples of 2 in square roots
Multiples of 3 in cube roots
Multiples of 4 in 4th roots
Steps to Adding and Subtracting Radicals
- Simplify all radicals
- Identify the radicals with the same index and same radicand
- For common radicals, add or subtract the coefficients and keep the common radical
Can Be Combined
Same index and radicand
Steps to Multiplying Radicals
- Multiply coefficients then use the product rule
- Simplify the resulting radical
Product Rule
n√an√b=n√ab
Do Not Distribute
Exponents
