Throughout Secondary Cycle 1, you were introduced to a few types of mathematical situations (proportional situations, inversely proportional situations, etc.), as well as several modes of representation (Cartesian plane, table of values, rule, etc.).
From Secondary 3 onwards, there is a distinction made between a relation and a function, and the notion of dependent and independent variables is clarified. Furthermore, the functional notation |f(x)| is used, and new ways of describing the graph of a function, called the properties of a function, are introduced.
Watch the following video to review all these concepts.
Relations and Functions
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A relation describes a link between two variables.
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A function is a relation between two variables where each value of the independent variable (starting set) is associated with only one value of the dependent variable.
In other words, if you draw a vertical line on the graph and it intersects the curve at a single point, it's a function. Otherwise, it's a relation.
Independent and Dependent Variables
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The independent variable, associated with the domain of the function, is the variable that is not affected by the others. It is commonly represented by the letter |x.|
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The dependent variable is always influenced by the independent variable. It is commonly represented by the letter |y.|
Functional Notation
Functional notation is used to identify the function using its independent variable. For example, instead of writing |y = 3x+5,| we write |f(x)=3x+5.| The dependent variable |y| is replaced by |f(x)|. It therefore refers to a function |f| whose independent variable is |x|.
Properties of Functions
Analyzing a function involves describing all the properties listed in the following table:
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Properties determined using |\boldsymbol{x}| |
Properties determined using |\boldsymbol{y}| |
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Domain Interval of all values that the independent variable can take. |
Range Interval of all values that the dependent variable can take. |
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X-Intercepts (Zeroes) The value(s) of |x| when |y| equals |0.|
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Y-Intercept (Initial value) The value of |y| when |x| equals |0|.
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Variation Intervals of |x| where the function is increasing, decreasing or constant. |
Extrema
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Sign |x| intervals when…
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