Warm-Up: Domain and Range of Graphs

Front

What is the definition of 'Domain' in the context of a function?

Back

The domain of a function is the complete set of possible values of the independent variable (usually x) for which the function is defined.

Front

What is the definition of 'Range' in the context of a function?

Back

The range of a function is the complete set of possible values of the dependent variable (usually y) that result from using the function.

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 has points. It includes all x-values that the graph covers.

Front

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

Back

The range can be determined by identifying the y-values for which the graph has points. It includes all y-values that the graph covers.

Front

What does it mean if a function has a domain of 0 ≤ x < 3?

Back

It means that the function is defined for all x-values starting from 0 up to, but not including, 3.

Front

What does it mean if a function has a domain of -1 ≤ x ≤ 4?

Back

It means that the function is defined for all x-values starting from -1 to 4, including both endpoints.

Front

What does it mean if a function has a range of -3 ≤ y ≤ 5?

Back

It means that the output values (y-values) of the function can take any value from -3 to 5, including both endpoints.

Front

What does it mean if a function has a domain of x > -3?

Back

It means that the function is defined for all x-values greater than -3, not including -3 itself.

Front

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

Back

An example is f(x) = 1/x, which is defined for all x except x = 0.

Front

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

Back

An example is f(x) = x^2, which has a range of y ≥ 0.