math final chap 5

5.1

100

a number that, when multiplied by itself twice, give the original number

square root

200

find the nth root when n=6 and a=729

(a)^1/n=3

300

evaluate: 32^2/5

4

400

4x²=64

4

500

What is the formula for the rate of depreciation when applying it to real life?

R=1-(s/c)^1/n 

where s is the value after depreciation, c is the original value, n is the life time, and r is the rate.

5.2

100

a^m . aⁿ = a^m+n

product of powers

200

which is product property and which is quotient property

(ab)^1/n= a^1/n X b^1/n

(a/b)^1/n= a^1/n/b^1/n

product property, quotient property

300

solve (625)^1/4

5

400

solve: 10(x)^1/7+ 2(x)^1/7=?

12(x)^1/7

500

simplify: (169c¹⁰)^1/2

13c⁵

5.3

100

describe the transformation

F(x)=(x+2)^1/2-3

left two units, down two units

200

square root functions and cubed root functions are examples of ______ functions?

Radical.

300

which is reflection in x axis and which is reflection in y axis

f(x)= -(3x)

f(x)= (-3x)

reflection in x axis, reflection in y axis.

400

what is the difference in writing a horizontal stretch and a vertical stretch

f(ax) 0>a>1, af(x) a>1

500

Describe the transformation

F(x)= (4x-8)^1/2-8

horizontal shrink by a factor of 1/4, move to the right 8 units, move down by 8 units.

5.4

100

When the equation is used to solve it, it can cause solutions that do not satisfy the original equation

Extra nuous solution

200

what is a radical equation

a mathematical sentence with a radical and an equal sign

300

3(x+2)^1/2=9

x=7

400

solve: (3x)^3/4-2=25

x=27

500

4(x)^1/2-3>/= 9

0</=x</=16

5.5 & 5.6

100

(f+g)(x)=? 

state the operation as well

F(x)+G(x), addition

200

(f+g)(x)= 

f(x)+g(x)

300

What is the horizontal line test?

Functions must be one-to-one to have inverse functions, horizontal line must intersect the graph no more than once.

400

subtract these functions

2x⁴-5x³+x²-6x

-(x⁴+4x³-x²+4x)

x⁴-9x³+2x²-10x

500

what is an inverse operation and what does it do

solves an operation for the opposite variable, undos math