Unit 4.1 & 4.2 - Understanding Set Builder Notation

Unit 4.1 & 4.2 - Understanding Set Builder Notation & Key Features from a Graph

School Year 2023-2024

Multiple Choice

Based on the definition of domain, what values can be used as an input for 𝑥 if 𝑦 = −4𝑥 + 7?

• all values greater than −5 and less than 5

• all values greater than −20 and less than 20

• It can not be determined

• any value

Multiple Choice

Based on the definition of domain, what values can be used as an input for 𝑥 if 8𝑥 − 5𝑦 = 15?

• all values greater than −5 and less than 5

• all values greater than −20 and less than 20

• it cannot be determined

• any value

Multiple Choice

Based on the definition of range, for the linear relationship 𝑦 = −4𝑥 + 7, what values are outputs for 𝑦?

• all values greater than −10 and less than 15

• all values greater than −20 and less than 20

• It cannot be determined

• any value

Multiple Choice

Based on the definition of range, for the linear relationship 8𝑥 − 5𝑦 = 15, what values are outputs for 𝑦?

• all values greater than −10 and less than 10

• all values greater than −20 and less than 20

• it cannot be determined

• any value

Multiple Choice

Write the following in set-builder notation

All real numbers

• $$\left\{x|-\infty<x<\infty\right\}$$

• $$\left\{x|-10<x<10\right\}$$

• $$\left\{x|x\ge0\right\}$$

• $$\left\{x|x<0\right\}$$

Multiple Choice

Write the following in set-builder notation

All real numbers that Less than or equal to -6

• $$\left\{x|-\infty<x<\infty\right\}$$

• $$\left\{x|-6<x<6\right\}$$

• $$\left\{x|x\ge-6\right\}$$

• $$\left\{x\ |\ x\le-6\right\}$$

Multiple Choice

Write the following in set-builder notation

All real numbers that greater than or equal to 5

• $$\left\{x|-\infty<x<\infty\right\}$$

• $$\left\{x|-5<x<5\right\}$$

• $$\left\{x|x\ge5\right\}$$

• $$\left\{x\ |\ x>5\right\}$$

Multiple Choice

Write the following in set-builder notation

All real numbers that greater than 11

• $$\left\{x|x\ge11\right\}$$

• $$\left\{x|x\le11\right\}$$

• $$\left\{x|x>11\right\}$$

• $$\left\{x\ |\ x<11\right\}$$

Multiple Choice

Write the following in set-builder notation

All real numbers that less than or equal to 8 and greater than or equal to -1

• $$\left\{x|-1<x<8\right\}$$

• $$\left\{x|-1\le x\le8\right\}$$

• $$\left\{x|-1<x\le8\right\}$$

• $$\left\{x|-1\le x<8\right\}$$

Multiple Choice

A research firm determined that the equation 𝑦 = 2𝑥 + 80 can be used to model the total amount of spending by tourists in Florida, 𝑦, in billions of dollars, for the years 2013-2017 where 𝑥 is the number of years since 2013. What is the domain?

• 2 ≤ 𝑥 ≤ 80

• 0 ≤ 𝑥 ≤ 4

• 0 ≥ x ≥ 4

• all real numbers

Multiple Choice

A research firm determined that the equation 𝑦 = 2𝑥 + 80 can be used to model the total amount of spending by tourists in Florida, 𝑦, in billions of dollars, for the years 2013-2017 where 𝑥 is the number of years since 2013. What is the range?

• 80 ≥ 𝑥 > 88

• 0 ≤ 𝑥 ≤ 88

• 80 < 𝑥 < 88

• 80 ≤ 𝑥 ≤ 88

Multiple Choice

A research firm determined that the equation 𝑦 = 2𝑥 + 80 can be used to model the total amount of spending by tourists in Florida, 𝑦, in billions of dollars, for the years 2013-2017 where 𝑥 is the number of years since 2013. What is the x-intercept?

• (80, 0)

• (-40, 0)

• (0, 80)

• (-60, 0)

Multiple Choice

A research firm determined that the equation 𝑦 = 2𝑥 + 80 can be used to model the total amount of spending by tourists in Florida, 𝑦, in billions of dollars, for the years 2013-2017 where 𝑥 is the number of years since 2013. What is the y-intercept?

• (0, 80)

• (80, 0)

• (-40, 0)

• (0, 40)