Algebra Unit 2: Lessons 8-11

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce. For example, if a function has outputs between -8 and 2, the range is -8 ≤ y ≤ 2.

Front

What is a function?

Back

A function is a relation that assigns exactly one output (y-value) for each input (x-value). For example, the set of pairs (6,-5), (7,-3), (8,-1), (9,1) is a function because no x-value is repeated.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) that the function can accept. For example, if a function is defined for x-values between -6 and 6, the domain is -6 ≤ x ≤ 6.

Front

What is an increasing interval in a function?

Back

An increasing interval is a range of x-values where the function's output (y-value) is rising as x increases. For example, if a function increases from x = 1 to x = 3, the increasing interval is (1, 3).

Front

What is a decreasing interval in a function?

Back

A decreasing interval is a range of x-values where the function's output (y-value) is falling as x increases. For example, if a function decreases from x = -∞ to x = 1, the decreasing interval is (-∞, 1).

Front

What is a mapping in mathematics?

Back

A mapping is a way to describe how each element of one set (domain) is paired with an element of another set (range). A mapping is a function if every input has exactly one output.

Front

What does it mean for a relation to be 'not a function'?

Back

A relation is 'not a function' if at least one input (x-value) is associated with more than one output (y-value). For example, the pairs (2,3) and (2,4) show that 2 is mapped to both 3 and 4, making it not a function.

Front

What is the difference between open and closed intervals?

Back

An open interval (a, b) does not include the endpoints a and b, while a closed interval [a, b] includes both endpoints. For example, (1, 3) is open, and [1, 3] is closed.

Front

How do you determine if a set of points represents a function?

Back

To determine if a set of points represents a function, check if any x-value is repeated with different y-values. If no x-value is repeated, it is a function.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, the graph does not represent a function.