The graph shows the amount (in dollars) an internet cafe charges its customers:
How much does Parvaneh have to pay if she uses their internet service for 2 hours and 40 minutes?
How much does Parvaneh have to pay if she uses their internet service for 4 hours?
What is the maximum number of hours that Parvaneh can use for \$15?
The graph shows the starting times of a shot put event for participants of different age groups:
What time will a 13 year old participant start their race?
Do any of the races start at half past the hour?
The graph shows the amount (in dollars) a lawyer charges for consultations:
How much does the lawyer charge for a 5.5 hour consultation?
How much does the lawyer charge for a 4 hour consultation?
What is the shortest possible consultation that the lawyer will charge \$800 for?
The graph shows the cost (in dollars) of a mobile phone call as a function of the length of the call:
How much does a call that lasts 4 minutes and 5 seconds cost?
How much does a 3-minute call cost?
What is the longest possible call that could be made for \$1.50?
What is the cost of each additional minute?
What is the initital connection cost?
The graph shows the parking costs (in dollars) over different lengths of time:
How much would 5 hours of parking cost?
What is the longest you can park your car for \$6?
The carpark offers a weekly pass for \$44. If Aaron parks his car for 6 hours each day, five days a week, how much would he save each week with the weekly pass?
The step graph shows the cost (in dollars) for postage of packages based on their weight:
Find how much it will cost to post a package that weighs:
1.7 kg
2.5 kg
0.5 kg
3.2 kg
If Neil has \$11, what range of package weights that he can afford to send?
What range of package weights can be sent for:
The cost (in dollars) of a train ticket, based on distance travelled (in km), is indicated by the step graph:
If Valentina needed to travel a distance of 11 km, how much would her train ticket cost?
Luke has a doctor's appointment 19 km away. How much money will he need for a round-trip ticket?
Sally needs to travel 4 km to get to the grocery store. How much will a one way ticket cost?
With \$3, if Dave buys a round-trip ticket, he can travel no further than what distance?
Maria commutes approximately 40 km each direction every day to work. Calculate the total cost for one week's worth (five days) of round-trip tickets.
The graph shows the cost (in dollars) of sending parcels of various weights overseas:
Find the cost of sending a letter weighing 100 grams.
Find the cost of sending a letter weighing 300 grams.
What is the heaviest letter that can be sent for \$2?
The graph shows the total cost of parking (in dollars) as a function of the number of hours parked:
How many free hours does this parking garage offer?
Peyvand goes to a movie and parks for 2.5 hours. How much will it cost her?
Tirdad works at the cinemas and parks for his entire 4.5-hour shift. How much will it cost him in parking?
The graph shows the cost per t-shirt (in dollars) when purchasing in bulk:
What is the cost per t-shirt when 45 t-shirts are bought in bulk?
What is the cost per t-shirt when 55 t-shirts are bought in bulk?
What is the most number of t-shirts that can be purchased at \$7.00 each?
The step graph shows the charges (in dollars) for a home phone plan:
How much will a 3-minute phone call cost?
How much will 4 phone calls, each longer than 1 minute but less than 2 minutes, cost?
A phone line user made the following calls during one month:
12 calls that were just under 2 minutes long each
13 calls just under 4 minutes long each
5 calls of less than 1 minute each
Find the total charges for the month to the nearest dollar.
Hiring helium tanks for balloons at a party costs \$20 up to and including the first hour, and \$5 per extra hour or any part thereof. Construct a step graph to represent the total cost for hiring helium tanks from 0 to 5 hours.
A telephone call is charged at \$0.70 for a call length of less than 1 minute, and \$0.20 extra per minute after that. Graph the cost of calls up to 5 minutes in length, with the vertical axis in dollars.
The cost of a train fare is calculated at \$1.30 for the first zone and then 20\text{c} per additional zone after that. Graph the fares for trips up to five zones, with the vertical axis in dollars.
A plumber charges a call-out fee of \$20 to come out to the site and on top of that, charges \$10 per 15 minute block on site or part thereof. Create a step graph that represents this scenario, with the vertical axis in dollars.
Create a step graph for the charge for sending parcels, where the vertical axis is in dollars:
| Express Post satchels (mm) | Maximum weight (g) | Charge per item |
|---|---|---|
| \text{Small } (220 \times 355) | 500 | \$2.50 |
| \text{Medium } (310\times405) | 3000 | \$4.25 |
| \text{Large } (435\times510) | 5000 | \$7.75 |
A hotel charges the following rates for hiring out their function room:
\$160 per hour for up to 2 hours inclusive.
\$120 per hour for more than 2 hours and up to 5 hours inclusive.
\$80 per hour for more than 5 hours and up to 10 hours inclusive.
Create a step graph that shows the amount charged per hour for the length of time the function room is booked.
Consider the graph of y = f \left( x \right), which is defined for all real x.
Define the function for x > 4.
Define the function for x \leq 4.
Consider the graph of y = f \left( x \right).
Is the function defined for all x?
Define the function for x > 4.
Define the function for x \leq 4.
Is the graph continuous at x = 4?
An insurance company charges a fixed monthly premium depending on which age group you fall into. The piecewise function outlines the premium, y, for a given age, x:
y = \begin{cases} \$112.17, & 18\lt x \leq 25 \\ \$128.72, & 25 \lt x \leq 35 \\ \$151.73, & 35 \lt x \leq 45 \\ \$176.27, & 45 \lt x \leq 55 \\ \$184.52, & 55 \lt x \leq 65 \\ \end{cases}
How much will the monthly premium for a 22-year old person be?
What could be the maximum age of someone who is paying \$176.27 per month for their premium?
Fikile held an insurance policy from when she turned 26 to when she turned 30. During this time, how much did she pay altogether in premiums?
If you are 35 years old, how much will your annual premium increase by once you turn 36 years old?
The government is looking at alternative taxation schemes and one proposal is to pay a fixed amount of tax depending on which income bracket you fall into.
The given piecewise function models the tax payable, y, based on an income of x:
y = \begin{cases} \$1200, & \$0 \lt x \leq \$15\,000 \\ \$4900, & \$15\,000 \lt x \leq \$35\,000 \\ \$12\,350, & \$35\,000 \lt x \leq \$65\,000 \\ \$43\,320, & \$65\,000 \lt x \leq \$114\,000 \\ \$54\,720, & x > \$114\,000 \\ \end{cases}
Under this proposal, how much tax will you pay on an income of \$14\,000?
What is the difference in income between the highest income earner and lowest income earner who are both paying \$43\,320 in tax? Assume you are taxed on whole dollars you earn.
Estelle is earning an income of \$63\,800. She is set to get a pay rise at the end of the year. What is the maximum pay rise she can get before falling into the next highest tax bracket?
At an indoor ski facility, the temperature is set to - 5 \degreeC at 2 pm. At 3 pm, the temperature is immediately brought down to - 12 \degreeC and left for 3 hours before immediately taking it down again to - 18 \degreeC, where it stays for the rest of the day’s operation. The facility operates until 10 pm.
Write a stepwise function that models the indoor temperature, y, at a certain time of the day, x hours after midday.
Sketch a graph of the step function relating time of day and temperature inside the ski facility.
Lakota entered the ski facility at 3:30 pm. What was the temperature inside the facility at this time?
Xavier wants to wait till the indoor temperature is - 7 \degreeC or lower. When is the earliest he can enter the facility?