1. Interval Notation: It is a way to represent intervals on the number line using brackets and parentheses. For example, an open interval from 2 to 5 would be represented as (2, 5), while a closed interval from -3 to 1 would be represented as [-3, 1].
Illustration:
Interval Notation: (2, 5)
Number line: (open interval from 2 to 5, excluding the endpoints)
2 5
2. Increasing vs Decreasing: This term refers to the behavior of a function as its input values increase or decrease. A function is considered increasing if, as the input values increase, the corresponding output values also increase. On the other hand, a function is considered decreasing if, as the input values increase, the corresponding output values decrease.
Illustration:
Increasing Function
y = x^2
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| \
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Decreasing Function
y = -x
/
/ \
/ \
---|----------- (x-axis)
3. Piecewise function: It is a function that is defined by multiple different formulas or rules, each applicable to different parts (or intervals) of the input values. These different formulas can be represented in separate equations or in a single equation with specific conditions specified for each part.
Illustration:
Piecewise Function:
f(x) =
x + 1 for x ≤ 1
x^2 for 1 < x ≤ 3
5x for x > 3
This piecewise function has different rules for different intervals of x. For x values less than or equal to 1, the function is defined as f(x) = x + 1. For x values between 1 and 3 (excluding 1), the function is defined as f(x) = x^2. For x values greater than 3, the function is defined as f(x) = 5x.
3 Vocabulary Terms - Define/Illustrate
1. Interval Notation 2. Increasing vs Decreasing 3. Piecewise function
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