Study Guide Piecewise and Radicals

Step 1: create 2 tables for each equation, using the assigned x-values

Step 2: Draw a dotted line at the x-value of domain
​Step 3: graph the points without crossing the dotted line
Step 4: closed circle if = to open if not

​Piecewise Functions

​x	​y
​1	​2
0​	2​
-1​	2​

​x	​y
​1	​1
2​	2​
3​	3​

Multiple Choice

If x>0, then?

• y=2

• y=1

• y=0

• y=-1

• y=-2

Multiple Choice

If x<0, then?

• y=2

• y=1

• y=0

• y=-1

• y=-2

Multiple Choice

Which graph corresponds to the piecewise function (pay close attention to the inequality signs)

Multiple Choice

Which graph corresponds to the piecewise function (pay close attention to the inequality signs)

Multiple Choice

Match the graph with the correct equation.

(*Hint: use the given domains to help)

Multiple Choice

USE WHAT YOU KNOW TO ANSWER:

Evaluate the function when x = 6 

• f(6) = -5
• f(6) = 4
• f(6) = 2
• f(6) = 7

​Radicals and Multiplication

Multiple Choice

• A
• B
• C
• D

Multiple Choice

• A
• B
• C
• D

Multiple Choice

• A
• B
• C
• D

Multiple Choice

Simplify

• √5
• -3√6
• √6
• 6

Multiple Choice

Simplify:
√10 ⋅ √45

• 3√50
• 8√2
• √450
• 15√2

Multiple Choice

Simplify:
√6 ⋅√6

• √36
• 2√3
• 12
• 6

Multiple Choice

Find the area of the rectangle shown.

• 18√20
• 12√10 + 6√2
• 9√12
• 36√5

​Radicals and Division

Multiple Choice

Simplify.

$$\frac{\sqrt{4}}{5\sqrt{16}}$$  

• $$\frac{1}{2}$$  

• $$\frac{1}{10}$$  

• $$10$$  

• $$1$$  

Multiple Choice

Simplify
$$\frac{7\sqrt{60}}{\sqrt{3}}$$

• $$14\sqrt{5}$$  

• $$5\sqrt{14}$$  

• $$14+\sqrt{5}$$  

• $$5+\sqrt{14}$$  

Multiple Choice

Divide:

• √12
• (4√3)/3
• √3
• (2√3)/3

Multiple Choice

Simplify:

• √5
• (√14)/2
• √7
• Cannot be simplified

Multiple Choice

​Radicals with Variables

Multiple Choice

Simplify the radical:

$$\sqrt{32x^3}$$  

• $$8x\sqrt{4x}$$  

• $$16x$$  

• $$16x\sqrt{x}$$  

• $$4x\sqrt{2x}$$  

Multiple Choice

Simplify the following:

$$\sqrt{28x^4y^4}$$  

• $$4x^2y^2\sqrt{7}$$  

• $$2x^2y^2\sqrt{7}$$  

• $$7xy\sqrt{4xy}$$  

• $$2xy\sqrt{7}$$  

Multiple Choice

Simplify the following:

$$\sqrt{32uv^4}$$  

• $$16v\sqrt{2u}$$  

• $$4v^2\sqrt{2u}$$  

• $$2v^2\sqrt{8u}$$  

• $$8uv^2$$  

Multiple Choice

Simplify the following:

$$3\sqrt{2x}\cdot\sqrt{2x^2}$$  

• $$3\sqrt{4x^3}$$  

• $$12x\sqrt{x}$$  

• $$6x\sqrt{x}$$  

• $$12x^3$$  

Multiple Choice

Simplify the following:

$$\sqrt{30x}\cdot-2\sqrt{5x^2}$$  

• $$-10x\sqrt{6x}$$  

• $$-2\sqrt{150x^3}$$  

• $$5x\sqrt{6x}$$  

• $$-2x\sqrt{35x}$$  

Multiple Choice

Simplify the following:

$$\sqrt{6k}\cdot\sqrt{7k^2}$$  

• $$k\sqrt{13k}$$  

• $$\sqrt{42k^3}$$  

• $$k\sqrt{42k}$$  

• $$6k\sqrt{7k}$$  

Multiple Choice

$$\sqrt{8xy^4}\cdot\sqrt{2x^2y^4}$$  

• $$4y^4\sqrt{x}$$  

• $$4xy^4\sqrt{x}$$  

• $$4xy^8\sqrt{x}$$  

• $$2xy^4\sqrt{2x}$$  

Multiple Choice

Divide and simplify.

• 4x√x
• 3x²/x³√36
• 2x
• 4x²

Multiple Choice

Simplify the following:

$$\frac{\sqrt{4m^4}}{5\sqrt{6m}}$$  

• $$\frac{2m}{5\sqrt{6m}}$$  

• $$\frac{\sqrt{2m^3}}{5\sqrt{3}}$$  

• $$\frac{2m^2\sqrt{6m}}{30m}$$  

• $$\frac{m\sqrt{6m}}{15}$$  

Multiple Choice

$$\frac{\sqrt{9xy}}{\sqrt{2x}}$$  

• $$\frac{x\sqrt{18y}}{2x}$$  

• $$\frac{\sqrt{18x^2y}}{2x}$$  

• $$\frac{3\sqrt{2y}}{2}$$