Table of a function
A festival ticket costs $15$ €. If you go with $1$, $2$ or $10$ friends, how much do you pay in total? The quickest way is to organise it in a table: one row with the number of tickets, another with the price. The table is another way of seeing the same function as the formula or the graph.
The table of values
Given the function defined by the algebraic expression $y = 3x - 2$, build a table of values by calculating the image ($y$) for the following values of the independent…
Given the function defined by the algebraic expression $y = 3x - 2$, build a table of values by calculating the image ($y$) for the following values of the independent variable:
$x = \{-2, -1, 0, 1, 2\}$.
You can do it on paper and send a photo with your answer.
From the formula to the table
If you know the formula, filling in the table means substituting each required value for $x$.
At a music festival, the price of a ticket is $15$ €. If we want to buy several tickets for a group of friends, the relationship between the number of tickets and the…
At a music festival, the price of a ticket is $15$ €. If we want to buy several tickets for a group of friends, the relationship between the number of tickets and the total cost can be organised in a table.
Complete the missing values in the following table of values:
| Number of tickets ($x$) | 1 | 2 | 3 | 4 | 10 |
|---|---|---|---|---|---|
| Total cost in € ($y$) | $15$ | ? | ? | $60$ | ? |
A video game streaming platform offers a premium plan that costs $5 \text{ €}$ per month as a fixed fee, plus $0,50 \text{ €}$ for each hour of high-quality gaming. The…
A video game streaming platform offers a premium plan that costs $5 \text{ €}$ per month as a fixed fee, plus $0,50 \text{ €}$ for each hour of high-quality gaming.
The function relating the monthly cost $y$ to the number of hours played $x$ is $y = 0,5x + 5$.
Complete the following table of values in your notebook to analyse the monthly expenditure:
| Hours played ($x$) | $0$ | $4$ | $10$ | $20$ | $35$ |
|---|---|---|---|---|---|
| Total cost ($y$) |
Is it proportional? The constant quotient
A table shows direct proportionality if, when you divide each $y$ by its $x$, the result is always the same number (the constant $m$).
A cyclist travels along a route at a constant speed of $20$ km/h. The following table shows the distance covered depending on the elapsed time: | Time in hours ($x$) |…
A cyclist travels along a route at a constant speed of $20$ km/h. The following table shows the distance covered depending on the elapsed time:
| Time in hours ($x$) | 0.5 | 1 | 1.5 | 2 | 3 |
|---|---|---|---|---|---|
| Distance in km ($y$) | $10$ | $20$ | $30$ | $40$ | $60$ |
From the table, state:
-
a) Which is the independent variable and which is the dependent variable?
-
b) Is it a continuous or discrete function? Reason your answer.
A group of friends wants to rent a country house that costs $240 \text{ €}$ for the weekend. The price each person must pay ($y$) depends on the number of people who go…
A group of friends wants to rent a country house that costs $240 \text{ €}$ for the weekend. The price each person must pay ($y$) depends on the number of people who go ($x$).
The table relating both quantities is the following:
| People ($x$) | $2$ | $3$ | $4$ | $5$ | $6$ | $8$ |
|---|---|---|---|---|---|---|
| Price per person ($y$) | $120$ | $60$ | $30$ |
- a) Fill in the missing values.
- b) Write the formula of the function.
- c) What type of function is it (linear, affine or inverse proportionality)?
From the table to the formula: the rate of change
If the table does not pass through the origin, it is not direct proportionality, but it may be affine ($y = mx + n$). To find $m$, look at how much $y$ goes up each time $x$ increases by one unit.
Given the following table of values for an affine function, find the missing values and determine the algebraic expression that defines it: | $x$ | -2 | -1 | 0 | 1 | 3 |…
Given the following table of values for an affine function, find the missing values and determine the algebraic expression that defines it:
| $x$ | -2 | -1 | 0 | 1 | 3 |
|---|---|---|---|---|---|
| $y$ | -11 | -5 | -2 |
a) Calculate the increase in $y$ for each unit increase in $x$ to find the gradient $m$.
b) Complete the gaps in the table based on the pattern found.
c) Write the algebraic expression of the function in the form $y = mx + n$.
A professional cyclist carries out endurance training. The table shows the distance covered as a function of time, but over different intensity sections: | Time ($h$) |…
A professional cyclist carries out endurance training. The table shows the distance covered as a function of time, but over different intensity sections:
| Time ($h$) | 0 | 1 | 1.5 | 2.5 | 4 |
|---|---|---|---|---|---|
| Distance ($km$) | 0 | 30 | 45 | 75 | 120 |
a) State whether the speed was constant throughout the training by analysing the increments in the table.
b) What distance will they have covered after $3 \text{ hours and } 15 \text{ minutes}$ if they maintain the same speed as in the last section?
c) Plot the points from the table on a coordinate system. Are all the points aligned on the same straight line passing through the origin?
You can do it on paper and send a photo with your answer.
Back to the start: For $1$, $2$ or $10$ tickets at $15$ € each, you pay $15$ €, $30$ € and $150$ € in total, values calculated with the formula $y = 15x$ that are clearly organised in the table.