Domain and Range of Graphs

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as f(x), where x is the input.

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

How do you determine the domain of a function from its graph?

Back

The domain can be determined by identifying the x-values for which the graph exists. Look for any breaks or restrictions in the graph.

Front

How do you determine the range of a function from its graph?

Back

The range can be determined by identifying the y-values that the graph reaches. Look for the highest and lowest points on the graph.

Front

What does it mean if a function is defined for all real numbers?

Back

If a function is defined for all real numbers, it means that there are no restrictions on the input values (x-values).

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What is an example of a function with a limited domain?

Back

An example is the square root function, f(x) = √x, which is only defined for x ≥ 0.

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What is an example of a function with a limited range?

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An example is the function f(x) = -x^2, which has a range of all real numbers less than or equal to 0.

Front

What notation is used to express the domain of a function?

Back

The domain can be expressed using interval notation, such as (-∞, 2] or [0, ∞).

Front

What notation is used to express the range of a function?

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The range can also be expressed using interval notation, such as [-4, 2) or (-∞, 5].