Topic 2 Review

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, the range of the function f(x) = x^2 is [0, ∞) because the output is always non-negative.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined. For example, the domain of the function f(x) = 1/x is all real numbers except x = 0.

Front

What does it mean for a mapping to be a function?

Back

A mapping is a function if each input (x-value) is associated with exactly one output (y-value). If an input is associated with more than one output, it is not a function.

Front

In the context of functions, what is the output?

Back

In a function, the output is the value that results from applying the function to an input. It is often represented by the variable y.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where for each input x, there is a unique output.

Front

What is the notation for the range of a function?

Back

The range is often denoted using interval notation. For example, the range [0, ∞) indicates that the output values start from 0 and go to infinity.

Front

What is the notation for the domain of a function?

Back

The domain is also expressed in interval notation. For example, the domain [-7, 5) indicates that the input values range from -7 to 5, including -7 but not including 5.

Front

How do you determine if a relation is a function?

Back

To determine if a relation is a function, use the vertical line test: if a vertical line intersects the graph at more than one point, it is 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.

Front

What is a vertical line test?

Back

The vertical line test is a method used to determine if a graph represents a function. If any vertical line crosses the graph more than once, it is not a function.