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MPM2D – Quadratic Functions – Functions. Any connection between two variables can be called a relation . A relation may be represented as a set of ordered pairs, a table of values, a graph, or an equation. MPM2D – Quadratic Functions – Functions.
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MPM2D – Quadratic Functions– Functions Any connection between two variables can be called a relation. A relation may be represented as a set of ordered pairs, a table of values, a graph, or an equation.
MPM2D – Quadratic Functions– Functions The set of first coordinates of the ordered pairs in a relation is called the domain. The elements of the domain are usually thought of as the independent variable or the x values. The set of second coordinates of the ordered pairs in a relation is called the range. The elements of the range are usually thought of as the dependent variable or the y values. Domain: Range:
MPM2D – Quadratic Functions– Functions A relation may also be a function if each x coordinate is connected with exactly one y coordinate. We can check for functions on a graph by using the vertical line test: If we can draw a vertical line that intersects the graph in more than one place, it is not a function. Since we can draw a vertical line that intersects this graph twice, it is not a function. Non-functions may be problematic due to the uncertainty associated with selecting a value for the independent variable.
MPM2D – Quadratic Functions– Functions A relation may also be a function if each x coordinate is connected with exactly one y coordinate. We can check for functions on a graph by using the vertical line test: If we can draw a vertical line that intersects the graph in more than one place, it is not a function. Since we cannot draw a vertical line that intersects this graph more than once, it is a function. For any given value of x, we can be certain of the value of y that will go with it.
MPM2D – Quadratic Functions – Functions For each of the following relations; i) state the domain and range using set notation, and ii) determine whether the relation is also a function 1) i) Domain: Range: ii) The relation is also a function because for every x value there is only one possible y value.
MPM2D – Quadratic Functions – Functions For each of the following relations; i) state the domain and range using set notation, and ii) determine whether the relation is also a function 2) i) Domain: Range: The relation is not also a function because for the x value of 2, there are two possible y values, 5 and 4. The points would line up vertically on a graph, so the relation would not pass the vertical line test.
MPM2D – Quadratic Functions – Functions 3) i) Domain: Range: The relation is also a function because it passes the vertical line test; regardless of where a vertical line is drawn it would only intersect the graph in one place.
MPM2D – Quadratic Functions – Functions 4) i) Domain: Range: The relation is not a function because it does not pass the vertical line test; at most elements of the domain, a vertical line would intersect the graph twice.
MPM2D – Quadratic Functions – Functions 5) i) Domain: Range: ii) The relation is also a function because it passes the vertical line test; regardless of where a vertical line is drawn it would only intersect the graph in one place.
