Algebra Chapter 7 Review

Simplifying Exponents

100

Anything to the 0 power is always...

What is 1?

200

x(x³)(x⁵)

What is x⁹?

300

(6x³y²)²

What is 36x⁶y⁴?

400

(a^-2)(b⁰)(c⁴)

What is c⁴/a²?

500

(12/2)(x/y⁵)(y⁴/x⁴)

What is 6/yx³?

Simplifying Square Roots

100

Square root of 4

What is 2?

200

Square root of 60

What is 2sqrt(15)?

300

Square root of 9x²

What is 3x?

400

Square root of 25x³y⁴

What is 5xy²sqrt(x)?

500

Square root of 45xy³z⁵

What is 3yz²sqrt(5xyz)?

Exponential Equations

100

The general form of an exponential equation

What is y=ab^x?

200

Is this an exponential equation: y=x²

What is no?

300

What is the initial value of this exponential equation: y=5^x

What is 1?

400

Is this growth or decay: y=2(1/3)^x

What is decay? 

500

Name the rate and determine whether it is growth or decay: y=3(4)^x

What is 4 and growth? 

Transformations

100

The transformation that occurred: f(x)= 4^x-3

What is down 3?

200

The transformation that occurred here: f(x)= -3^x

What is vertical reflection/over x-axis?

300

The transformations that occurred here: f(x)= 3(2)^2x

What is vertical stretch by 3 and horizontal compression by 2?

400

The transformations that occurred here: 

f(x)= 2^1/2x-3+4

What is horizontal stretch by 1/2, left 3, and down 4?

500

The transformations that occurred here:

 f(x)= 3(4)^-x-4+2

What is vertical stretch by 3, horizontal reflection/over y-axis, right 4, and up 2?

Sequences/Recursive Formulas

100

Is this geometric or arithmetic? 

1, 4, 16, 64

What is geometric?

200

The first 4 terms of this recursive sequence:

a₁=2, a_n=a_n-1+3

2, 5, 8, 11

300

The recursive formula for this sequence:

1, 4, 16, 64

What is a₁=1, a_n=a_n-1(4)?

400

The geometric sequence formula for this sequence:

27, 9, 3, 1

What is a_n=27(1/3)^n-1?

500

The geometric sequence formula for this sequence: 

256, 128, 64

What is a_n=256(1/2)^n-1?