Functions, domain and Range

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input from its domain.

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.

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.

Front

What does the vertical line test determine?

Back

The vertical line test determines if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.

Front

How do you find the output of a function for a given input?

Back

To find the output, substitute the input value into the function's equation and simplify.

Front

What is the difference between an open interval and a closed interval?

Back

An open interval does not include its endpoints, while a closed interval includes its endpoints.

Front

What is the notation for the domain of a function?

Back

The domain is often expressed in interval notation, such as (-∞, ∞) or [a, b].

Front

What is the notation for the range of a function?

Back

The range is also expressed in interval notation, such as [c, d) or (-∞, b].

Front

If f(x) = 3x - 5, what is f(2)?

Back

f(2) = 3(2) - 5 = 6 - 5 = 1.

Front

If the function is defined as f(x) = x^2, what is the range of f?

Back

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