Domain & Range
A function tracks the number of students in a cafeteria from noon to 2 PM. Should the domain include decimals like 1.5 hours?
Yes, time can be measured continuously (like 1:30 PM = 1.5 hours after noon)
What is |−7|?
7
If f(x) = 3x, what operation undoes multiplication by 3?
Division by 3 (so f⁻¹(x) = x/3)
Give a real-world example of a piecewise function.
Tax brackets, shipping costs based on weight, parking fees by hour, overtime pay, etc.
If g(5) = 12, what point is on the graph of g?
(5, 12)
The same cafeteria function shows student count ranging from 15 to 120. Can the range include 87.3?
No, you cannot have 87.3 students - range should be whole numbers only
An oven target temperature is 350°F. If the actual temperature is 355°F, what's the absolute error?
5 degrees
A function m = 50h converts hours to miles driven. What does the inverse function tell you?
Hours driven based on the number of miles traveled
A streaming service costs $10/month for 1 screen, $15 for 2-3 screens, $20 for 4+ screens. Is this piecewise?
Yes - different prices for different intervals of screens
A function T(d) = 2d + 10 gives trip time in minutes from distance in miles. What does the 10 represent?
10 minutes of fixed time (like getting ready/parking) before distance matters
A parking lot function shows cars from 0 to 200 over a 12-hour period. What makes sense for domain and range?
Domain: all numbers 0 to 12 (time is continuous); Range: whole numbers 0 to 200 (can't have partial cars)
For target temp 350°F, write a function e(t) for absolute error when actual temperature is t.
|t-350|
For m = 50h, write the inverse function.
h = m/50 or h = 0.02m
Taxi fare: $5 base + $2 per mile for first 10 miles, then $1.50 per mile after. What's the fare for 8 miles?
$21 (5 + 2×8 = 5 + 16 = 21)
A function T(d) = 2d + 10 gives trip time in minutes from distance in miles. In T(d) = 2d + 10, what does the coefficient 2 mean?
It takes 2 minutes per mile traveled
A function models plant height in cm over 30 days. Height goes from 5 cm to 23 cm. Describe the appropriate range.
All numbers from 5 to 23 (height can be any value like 12.7 cm, it's continuous)
If |x - 5| = 3, what are the two possible values of x?
x = 8 or x = 2
Using m = 50h, if someone drove 225 miles, how many hours did they drive?
4.5 hours (225 = 50h, so h = 225/50 = 4.5)
Taxi fare: $5 base + $2 per mile for first 10 miles, then $1.50 per mile after. What's the fare for 15 miles?
$32.50 (First 10 mi: 5 + 20 = 25; Next 5 mi: 1.50×5 = 7.50; Total: 32.50)
A function T(d) = 2d + 10 gives trip time in minutes from distance in miles. For T(d) = 2d + 10, find T⁻¹(30).
What real-world information does T⁻¹(30) = 10 give you in the trip context?
Why would a domain be restricted to whole numbers from 1 to 52 instead of all numbers?
The context requires discrete values (like cards in a deck, cant have 1.5 cards)
A machine must cut boards to exactly 48 inches. If |L - 48| = 0.25, what are the acceptable lengths?
47.75 inches or 48.25 inches
If P(w) = 15w + 50 gives pay from weeks worked, find and interpret P⁻¹(200).
P⁻¹(200) = 10 weeks. This means earning $200 requires working 10 weeks.
A phone plan charges $0.10/min for first 100 minutes, free after. Max 300 min/month. What's the range?
All values from $0 to $10 (could be any amount like $4.30 for 43 minutes)
A function T(d) = 2d + 10 gives trip time in minutes from distance in miles. What real-world information does T⁻¹(30) = 10 give you in the trip context?
If your total trip time was 30 minutes, you traveled 10 miles