3 Vocabulary Terms - Define/Illustrate
1. Function Notation 2. Vertical Line test 3. Independent vs Dependent variable
1. Function Notation: Function notation is a way of representing a mathematical function with symbols. It typically involves using the letter "f" followed by parentheses to denote the input variable. For example, if f(x) represents a function, "f(2)" would mean plugging in the value 2 for the variable x.
Illustration:
Let's say we have a function f(x) = 2x + 3. If we want to find the value of the function when x is equal to 4, we would use function notation and write f(4) = 2(4) + 3 = 11.
2. Vertical Line Test: The vertical line test is a graphical test used to determine if a relation is a function or not. It involves drawing vertical lines on a graph and seeing if any of the lines intersect the graph in more than one place. If a vertical line intersects the graph in multiple places, then the relation is not a function. However, if every vertical line intersects the graph at most once, then the relation is a function.
Illustration:
In the image below, the graph on the left passes the vertical line test because each vertical line intersects the graph at most once, indicating that it represents a function. On the other hand, the graph on the right fails the vertical line test because there is a vertical line that intersects the graph in two places, indicating that it does not represent a function.
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Graph that passes the vertical line test: Graph that fails the vertical line test:
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______|__|_______ ______|__|_______
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3. Independent vs Dependent variable: In mathematics and science, variables are often categorized as either independent or dependent variables. An independent variable is a variable that is changed or controlled in an experiment or equation to observe the effect on the dependent variable. On the other hand, a dependent variable is a variable whose value depends on the independent variable.
Illustration:
Let's say we are conducting an experiment to see how the amount of water given to plants affects their growth. In this case, the amount of water would be the independent variable because we are adjusting and controlling its value. The growth of the plants would be the dependent variable because it depends on the amount of water given.
To illustrate this, in a graph plotting the amount of water given (independent variable) on the x-axis and the growth of plants (dependent variable) on the y-axis, we would see the growth of plants change as the amount of water is altered. This shows the relationship between the independent and dependent variables.