Domain and Range

Front

What is the definition of 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 definition of 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 given a set of ordered pairs?

Back

The domain can be determined by listing all the unique x-values from the ordered pairs.

Front

How do you determine the range of a function given a set of ordered pairs?

Back

The range can be determined by listing all the unique y-values from the ordered pairs.

Front

What is the vertical line test?

Back

The vertical line test is a method used 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.

Front

What does it mean if a graph passes the vertical line test?

Back

If a graph passes the vertical line test, it means that for every x-value, there is exactly one corresponding y-value, confirming that it is a function.

Front

What is an example of a function that fails the vertical line test?

Back

An example of a function that fails the vertical line test is a circle, as vertical lines can intersect the circle at two points.

Front

What is the domain of the function represented by the graph of a line that extends from -4 to 3?

Back

The domain of the function is the interval -4 ≤ x ≤ 3.

Front

What is the range of the function represented by the ordered pairs {(0,1), (1,-3), (2,-4), (-4,1)}?

Back

The range of the function is {-4, -3, 1}.

Front

What is the significance of identifying the domain and range in real-world applications?

Back

Identifying the domain and range helps in understanding the limitations and possible outputs of a function in real-world scenarios.