Meeting Functions

'Get to the heart of what functions are about by matching these inputs, equations and outputs together - a 'simple' matching activity!'

There are 8 algebraic equations giving the relationship between the variables ‘x’ and ‘y’. There are 8 sets of input values (x values or ‘domain’) and 8 sets of corresponding output values (y values or ‘range’). The task is to make 8 sets of 3 including one of each type (1 set of input values, 1 equation and 1 set of output values). Of course the input values could go into almost all of the equations so the challenge is to put them in to an equation that will generate one of the given sets of output values.

It is easy to study functions and forget what they are all about. Equations where 'y' is dependant on 'x' all work on the principal that for given 'x' values there are corresponding 'y' values. The function describes what you have to do with the 'x' values to generate the 'y' values. These pairs of values then correspond to points on a coordinates grid and together make the graph of the equation or function. This activity involves matching a given set of input values with an equation and a corresponding set of output values to practise this fundamental point. Below is a quick screencast to demonstrate the point of the activity.

Resources

You need the worksheet  Meeting Functions. There are teacher notes  Meeting functions available as well. Further descriptions and examples of the activity are available below.

Below are a few photographs of 'Meeting functions' in action

The Cards

x = {4,9,16}

y = x²

y = {7}

x = {-3,-2,-1,0,1,2,3}

y = x3

y = {-4,-3,-1}

x = {-3,-2,-1,0,1,2,3}

y = x0.5

y = {-12,-2,0,4 }

x = {-2,-1,0,1,2}

y = 3x + 1

y = {13,28,49}

x = {16,9,1}

y = -2x + 7

y = {-25,-11,-9,-1,23,39 }

x = {-3,-1,0,1,2,4}

y = x²+ 5x + 6

y = {0,1,4,9 }

x = {-16,-8,4,8,9,16}

y = x3 - x²

y = {0,2,6,12,20,30 }

x = {-3,-2,-1,0,1,2,3}

y = 7

y = {-27,-1,0, 8,64 }

What to do?

Above, there are 8 algebraic equations giving the relationship between the variables ‘x’ and ‘y’. There are 8 sets of input values (x values or ‘domain’) and 8 sets of corresponding output values (y values or ‘range’). The task is to make 8 sets of 3 including one of each type (1 set of input values, 1 equation and 1 set of output values). Of course the input values could go into almost all of the equations so the challenge is to put them in to an equation that will generate one of the given sets of output values.

An Example

If the set of input values

x = {1, 2, 3}

was put into the equation

y = 2x2

they would generate the corresponding set out output values

y = {2, 8, 18}

Over to you

Now create 8 sets of 3 from the cards above.

  • You could cut them out and rearrange them
  • Copy them out in the correct order
  • Copy and paste them into the correct order if working digitally

Description

  • Students are given the 'Meeting Functions' worksheet. The task is quite self explanatory but teachers may want to help by showing an example. There is also a screencast above to help.
  • Students should compare solutions with each other to help find errors and justify answers.
  • Students should share their conclusions with each other.
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