You are going to choose a number, multiply it by 5, and subtract the answer from 50.
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Choose any number from set A and do the above calculations.
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Choose any number from set B and do the above calculations.
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If you choose any other number from set B, do you think the answer will also be a negative number?
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Write down all the different output numbers that will be obtained when the calculations 50−5x are performed on the different numbers in set A.
Output numbers are numbers that you obtain when you apply the rule to the input numbers.
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Write down the output numbers that will be obtained when the formula 50−5x is applied to set B.
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Complete the following table for set A:
Input numbers
1
2
3
4
5
6
7
8
9
Values of 50−5x
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Complete the following table for set B:
Input numbers
20
30
40
50
60
70
80
90
Values of 50−5x
In this question your set of input numbers will be the even numbers 2; 4; 6; 8; 10; ...
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What will all the output numbers be if the rule 2n+1 is applied to the set of even numbers? Write a list.
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What will the output numbers be if the rule 2n−1is applied?
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What will the output numbers be if the rule 2n+5 is applied?
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What will the output numbers be if the rule 3n+1 is applied?
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What kind of output numbers will be obtained by applying the rule x−1000 to natural numbers smaller than 1 000?
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What kind of output numbers will be obtained by applying the rule x10+10 to natural numbers smaller than 10?
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If you use the rule 30x+2, and use input numbers that are positive fractions with denominators 2, 3 and 5, what kind of output numbers will you obtain?
A quantity that changes is called a variable quantity or just a variable.
If one variable quantity is influenced by another, we say there is a relationship between the two variables. You can sometimes work out which number is linked to a specific value of the other variable.
The output number can also be called the output value, or the value of the expression, which is 10x+5 in this case.
Arelationship between two variables in which there is only one output number for each input number, is called a function.
- With a table that shows some values of the two variables. A table shows clearly which value of the output variable corresponds to each particular value of the input variable.
- A flow diagram, which shows what calculations are to be done to calculate the output number that corresponds to a given input variable.
- A formula, which also describes what calculations are to be done to calculate the output number that corresponds to a given input variable.
- A graph.
Complete the flow diagram:
A completed flow diagram shows two kinds of information:
- It shows what calculations are done to produce the output numbers.
- It shows which output number is connected to which input number.
The output numbers of a function are also called function values. Hence the formula can also be written as
function value = 5x+20
Complete this table for the function described by 5x+20:
|
Input numbers |
-1 |
-2 |
-3 |
-4 |
-5 |
|
Function values |
Draw a graph of this function below.
A graph of a certain function is given below. Complete the table for this function.
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Input numbers |
|||||
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Function values |
a flow diagram
a table of values for the set of integers from -5 to 5
a graph
The relationship described by the expression 3x+4
The relationship described by the expression 2x−5
The relationship described by the expression 12x+2
The relationship described by the expression −3x+4
The relationship described by the expression 2,5x+1,5
The relationship described by the expression 0,2x+1,4
The relationship described by the expression −2x−4
