Podcast
Questions and Answers
To emphasize the slow increase in profits, it would be best for Bradley to use ___________ for his presentation.
To emphasize the slow increase in profits, it would be best for Bradley to use ___________ for his presentation.
graph A
The relationship between the number of months after the first year and the amount remaining on the card is __________.
The relationship between the number of months after the first year and the amount remaining on the card is __________.
discrete
What are the domain and range of the relation?
What are the domain and range of the relation?
0 ≤ x ≤ 70, 0 ≤ y ≤ 500
Which graph models the piecewise function for the toy packaging company situation?
Which graph models the piecewise function for the toy packaging company situation?
Which graph has the most appropriate scales and units for the cost of renting a community center?
Which graph has the most appropriate scales and units for the cost of renting a community center?
Describe the distance traveled between 10 minutes and 15 minutes.
Describe the distance traveled between 10 minutes and 15 minutes.
Based on the graph, which statement is true?
Based on the graph, which statement is true?
Which of the following represents a function?
Which of the following represents a function?
A particular strain of a common bacteria replicates itself every 14 minutes. What does this situation represent?
A particular strain of a common bacteria replicates itself every 14 minutes. What does this situation represent?
What is the domain of the set of ordered pairs: (-1,1), (0,-1), (5,-11), (10,-21)?
What is the domain of the set of ordered pairs: (-1,1), (0,-1), (5,-11), (10,-21)?
Which of the following does Ronnie's data represent?
Which of the following does Ronnie's data represent?
Which of these graphs represents a function?
Which of these graphs represents a function?
What is the range of the function shown on the graph?
What is the range of the function shown on the graph?
Given the domain {-4, 0, 5}, what is the range for the relation 12x + 6y = 24?
Given the domain {-4, 0, 5}, what is the range for the relation 12x + 6y = 24?
Let d(t) be the total number of miles Joanna has cycled, and let t represent the number of hours after stopping for a break during her ride. d(t) = 12t + 20. So, d(4) = __________. This means that after ____________, Joanna ____________.
Let d(t) be the total number of miles Joanna has cycled, and let t represent the number of hours after stopping for a break during her ride. d(t) = 12t + 20. So, d(4) = __________. This means that after ____________, Joanna ____________.
Which function has the same graph as x + y = 11?
Which function has the same graph as x + y = 11?
Find the value of h(-7) for the function h(x) = 5.7 - 19x.
Find the value of h(-7) for the function h(x) = 5.7 - 19x.
Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45, select the statement that could be true for g.
Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45, select the statement that could be true for g.
Find the value of g(7) for the function g(x) = 7/8x - 1/2.
Find the value of g(7) for the function g(x) = 7/8x - 1/2.
What domain and range are reasonable for the function W(b) = 12b given that Owen has enough materials to build up to 10 birdhouses?
What domain and range are reasonable for the function W(b) = 12b given that Owen has enough materials to build up to 10 birdhouses?
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Study Notes
Functions and Graphs
- Profits of competitors increased slowly over 16 months, emphasized through graph A as it appears to increase less.
- Cash card starts at $25; value decreases by $2.50 each month after the first year. This relationship is discrete with independent variable as time (months) and dependent variable as remaining value.
- Water heater drains 100 gallons in 20 minutes, then 200 gallons in the following 20 minutes, closed for a 10-minute break. Domain: 0 ≤ x ≤ 70, Range: 0 ≤ y ≤ 500.
Piecewise Functions
- Toy packaging: 80 boxes/hour for first 3 hours, 2-hour training break, then 20 boxes/hour for 4 hours. The function is represented by points (0, 0), (3, 240), (5, 240), (9, 320).
- Community center rental: $100 base cost plus $10 per guest. Appropriate graph scales: y-axis for rental costs ($100 to $500), x-axis for guest count (10 to 50).
Distance and Rate
- Jacob's road trip covers 10 miles in 15 minutes; during the first 10 to 15 minutes, distance traveled is increasing.
Relations and Functions
- Relationship between the number of crates and total price is important for analysis.
- Functions represented by ovals: -4 to 5 paired with 9, 3, 13, and 7.
- Bacterial replication occurs every 14 minutes; this is both a relation and a function.
- Survey on siblings and pets shows only a relation, not a function.
Domain and Range
- Given ordered pairs (-1, 1), (0, -1), (5, -11), (10, -21); domain is {-1, 0, 5, 10}.
- Function from graphical representation has range of 9 ≤ y ≤ 8.
- Given a function 12x + 6y = 24, domain of {-4, 0, 5} results in a range of {12, 4, -6}.
Function Evaluation
- For Joanna's cycling function d(t) = 12t + 20, d(4) = 68, indicating 68 miles cycled after 4 hours.
- For the linear equation x + y = 11, an equivalent function is f(x) = -x + 11.
- Function h(x) = 5.7 - 19x evaluated at h(-7) yields 138.7.
- g(x) = 7/8x - 1/2 evaluated at g(7) results in 45/8.
- g has a domain of -20 ≤ x ≤ 5 and range of -5 ≤ g(x) ≤ 45, with potential values like g(-13) = 20 being possible.
Resource Management
- Owen can build up to 10 birdhouses needing 12 square feet each; function W(b) = 12b with domain 0 ≤ b ≤ 10 and range 0 ≤ W(b) ≤ 120.
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