For Questions 1–4, it can be helpful to organise your answers into a table like this:
0 | 1 | 2 | 3 | 4 | 5 | 6 |
If an answer is undefined, you can leave your answer as “undefined” or “DNE” (which stands for “Does Not Exist”).
For an extra challenge in Questions 1–3, try finding the range of each function!
Evaluate each function for
Solution:
Domain:
Range:
Solution:
Domain:
Range:
Solution:
Domain:
Range:
Solution:
Domain:
Range:
Solution:
Domain:
Range:
Solution:
Domain:
Range:
Evaluate each function for
Solution:
Domain:
Range:
Solution:
Domain:
Range:
Solution:
Domain:
Range:
Solution:
Domain:
Range:
Solution:
Domain:
Range:
Solution:
Domain:
Range:
Evaluate each function for
Solution:
Domain:
Range:
Solution:
Domain:
Range:
Solution:
Domain:
Range:
Evaluate each function for
Solution:
DNE |
Domain:
Solution:
DNE |
Domain:
Solution:
Domain:
Solution:
DNE |
Domain:
Solution:
Domain:
Solution:
DNE |
Domain:
The cost of a taxi ride is a base rate of $3.50 plus $1.50 per kilometre travelled.
Express the cost of a taxi as a function. Use
Solution:
Calculate the cost of a 10km trip.
Solution: The trip is 10km long, so we
have
Calculate the cost of a 175km trip.
Solution: The trip is 175km long, so we
have
What is the domain of the function
Solution: It doesn’t make sense to travel
a negative distance (but any non-negative distance is fine), so the
domain is
What is the range of the function
Solution: The domain is
At a particular buffet restaurant, it costs each person $26 to eat dinner. The restaurant also charges a fee of $0.30 for every 100g of leftover food at the end of the meal.
Express the total cost of a meal as a function. Use
Solution:
Calculate the total cost of a meal, where the person leaves 100g of leftover food.
Solution: The person had 100g of leftover
food, so
Calculate the total cost of a meal, where the person leaves no leftover food.
Solution: The person had 0g of leftover
food, so
Calculate the total cost of a meal, where the person leaves 670g of leftover food.
Solution: The person had 670g of leftover
food, so
What is the domain of the function
Solution: It doesn’t make sense to leave
behind a negative amount of food (but you can leave behind any
non-negative amount of food), so the domain is
What is the range of the function
Solution: The domain is
A farmer is planning to purchase some straight fencing to build an enclosed pasture for their chickens. Each metre of fencing costs $10 to purchase and install.
Construct a function that takes in the farmer’s budget, which is
the amount of money they plan to spend purchasing fencing, and outputs
the maximum area of the pasture that could be built. Use
Solution:
The area is the side length of the pasture squared. Since a square has four sides, the side length is the total amount of fencing purchased, divided by four. Since each metre of fencing costs $10, the total amount of fencing purchased is the amount of money spent, divided by ten.
What is the area of the largest pasture that could be constructed with a budget of $200?
Solution: The amount of money spent would
be $200, so
What is the area of the largest pasture that could be constructed with a budget of $1000?
Solution: The amount of money spent would
be $1000, so
What is the domain of the function
Solution: It doesn’t make sense to spend a
negative amount of money (but any non-negative amount of money is fine),
so the domain is
What is the range of the function
Solution: The domain is