Algebra II C Chapter 7 warm ups and
instructions
A2C 7.1 warm up
Solve the equation. Round your answer to
two decimal places when appropriate.
1. 𝟓𝒙𝟑 = 𝟑𝟔𝟓𝟎
2. (𝟑𝒙 + 𝟐)𝟑 = 𝟐𝟎
3. 𝟑𝒙𝟒 + 𝟐 = 𝟓
4. (𝟐𝒙 − 𝟕)𝟔 = 𝟏𝟐𝟎
A2C 7.2 warm up #1
Using Properties of rational exponents
Simplify the expression
𝟓
𝟑
1. 𝟑 ∙ 𝟑
𝟒
𝟑
𝟒
𝟏 𝟑
𝟒
2. (𝟕 )
3.
𝟐
𝟕𝟓
𝟕
Using Properties of radicals
A radical with index n is in simplest form if
there are no perfect nth powers in the
radicand, no fractions under the radical sign,
and no radicals in any denominator. To write
a radical in simplest form, apply the properties
of radicals, remove any perfect nth powers
(other than 1), and rationalize any
denominators.
Product and Quotient properties of radicals
𝒏
𝒏
𝒏
Product property: √𝒂 ∙ 𝒃 = √𝒂 ∙ √𝒃
Quotient property:
𝒂
√𝒃
𝒏
𝒏
=
√𝒂
𝒏
√𝒃
Simplify the expression
𝟒
1. √𝟏𝟔𝟐
𝟓
𝟑
3.
√𝟓𝟒
𝟑
√𝟗
𝟓
2. √𝟓𝟔 × √𝟏𝟐
𝟑
4.
√𝟓𝟔
𝟑
√𝟑
Two radical expressions are like radicals if they
have the same index and the same radicand.
A2C 7.2 warm up #2
Simplify the expression.
𝟑
𝟑
1. √𝟏𝟐 + 𝟑 √𝟏𝟐
2. √𝟐𝟕 + 𝟐√𝟕𝟓
𝟑
𝟑
𝟑
3. √𝟓𝟒 + √𝟒𝟎 + √𝟏𝟔
A2C 7.2 warm up #3
Simplify. Assume all variables are positive.
1. √𝟏𝟐𝒙𝟓
𝟑
2. √𝟏𝟔𝒄𝟒
3.
𝒚𝟐
√ 𝟓
𝒙
A2C 7.3 warm up #1
Read page 415 and the top half of page 416
and then do the following problems.
1. Find 𝒇(𝒙) + 𝒈(𝒙) and𝒇(𝒙) − 𝒈(𝒙).
Simplify your answers.
𝒇(𝒙) = 𝟑𝒙𝟑 − 𝟐𝒙𝟐 + 𝟓𝒙 − 𝟏
𝒈(𝒙) = 𝒙𝟐 + 𝟓𝒙 − 𝟏
2. Find𝒇(𝒙) ∙ 𝒈(𝒙). Simplify your answer.
𝒇(𝒙) = −𝒙𝟐 + 𝟐𝒙 + 𝟐
𝒈(𝒙) = 𝒙 + 𝟏
3. Find
𝒇(𝒙)
.
𝒈 ( 𝒙)
Simplify your answer.
𝒇(𝒙) = 𝟑𝒙 + 𝟓
𝒈(𝒙) = 𝟐𝒙𝟐 − 𝟏
Composition of Functions - Domains
Rules for excluding numbers from the
domain of 𝒇(𝒈(𝒙))
1. If x is not in the domain of g, it is
not in the domain of 𝒇(𝒈(𝒙))
2. Any x for which 𝒈(𝒙) is not in the
domain of f must not be in the
domain of 𝒇(𝒈(𝒙)).
A2C 7.3 warm up #2
𝟏⁄
𝟒𝒙 𝟐
Let 𝒇(𝒙) =
and 𝒈(𝒙) = 𝒙 + 𝟑. Perform
the given operation and state the domain.
1. 𝒇(𝒙) − 𝒈(𝒙)
2. 𝒈(𝒇(𝒙))
3. 𝒇(𝒈(𝒙))
4. 𝒇(𝒙) ∗ 𝒈(𝒙)
Review topics for 7.1 – 7.3 quiz
 Definitions: power function, composition
of function f with function g
 Changing expressions from rational to
radical notation
 Simplifying radical and rational
expressions
 Adding and subtracting radical and
rational expressions
 Finding combinations of functions and
their domains
 Solving equations involving power
functions