Grade 9 Functions & Relationships

FUNCTIONS & RELATIONSHIPS

Grade 9 Term 03

Functions & Relationships

• Functions and relationships were also done in Term 1. The focus in this term is on finding output values for given equations, and recognising equivalent forms between different descriptions of the same relationship.

• The purpose of this topic is to develop a firm understanding of the relationship between the input (x) and output (y) and to recognise that the output is unique for each specified input.

• It is important to note that the skills covered in Term 3 are much the same as in Term 1, but graphs will be introduced as another way of representing a function.

​Glossary of Terms

• Function: A mathematical condition or rule linking the input to the output.

• Relation: A relation is a relationship between sets of values. In maths, the relation is between the x-values and y-values of ordered pairs

• Input: The number/value that was chosen to replace the variable in an expression.

• Output: The output is dependent on the input – it is the answer once the operation has been

  performed according to the expression given.

• Equation: A mathematical sentence built from an algebraic expression using an equal sign.

  Example: 2a + 3 = 10

• Expression: A mathematical model which represents a situation. It can include variables (letters), constants and operations.

  Example: 2b + 3c

​....Glossary of Terms

• Flow diagram: A diagram representing a sequence of movements to be performed on a given value.

• Algebraic Rule: An expression representing a rule to be performed on the variable.

  Example: 3m + 1 (Multiply the number represented by ‘m’ by 3 then add 1 to the answer)

• Inverse operation: The opposite operation that will ‘undo’ an operation that has been performed.

  Addition and subtraction are the inverse operation of each other. Multiplication and Division are the inverse operation of each other.

Equations

In this section you will find numbers that make statements true. This is called solution of equations. You will solve equations in two different ways, by inspection and by ‘reversing’ them.

You will also find that two equations can have the same solution. Such equations are called equivalent equations. You will also discover that not all statements are algebraic equations. Some statements are algebraic identities and others are in fact algebraic impossibilities. You will learn what the difference is between these three types of statements.

​Solving Equations

The below is an example of an algebraic equation:

​2x+3=5x+3

Solving equations by inspection

​Seven equations are listed in the table. Use the table to find out for which of the given values of x it will be true that the left-hand side of the equation is equal to the right-hand side.

In each of the equations, substitute the x equivalent to solve the equation.

Fill in the Blank

Solve the equation 5x − 4 if x=2.

Fill in the Blank

Solve the equation 5 − 3x if x=3.

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Fill in the Blank

Solve the equation 5 − 4x if x=2.

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Fill in the Blank

Solve the equation 11x − 15 if x=2.

Solving equations by inspection

​Seven equations are listed in the table. Use the table to find out for which of the given values of x it will be true that the left-hand side of the equation is equal to the right-hand side.