Domain and Range of Continuous Graphs

Front

What is the RANGE of a continuous graph?

Back

The RANGE is the set of all possible output values (y-values) of a function. For example, if a graph has a range of -3 ≤ y ≤ 5, it means y can take any value from -3 to 5.

Front

What is the DOMAIN of a continuous graph?

Back

The DOMAIN is the set of all possible input values (x-values) of a function. For example, if a graph has a domain of -4 ≤ x ≤ 1, it means x can take any value from -4 to 1.

Front

How do you determine the RANGE from a graph?

Back

To determine the RANGE from a graph, look at the lowest and highest points on the y-axis that the graph reaches. This gives you the minimum and maximum y-values.

Front

How do you determine the DOMAIN from a graph?

Back

To determine the DOMAIN from a graph, look at the leftmost and rightmost points on the x-axis that the graph reaches. This gives you the minimum and maximum x-values.

Front

What does it mean if the DOMAIN is 'All real numbers'?

Back

If the DOMAIN is 'All real numbers', it means that the function can accept any value of x without restrictions.

Front

What does it mean if the RANGE is 'All real numbers'?

Back

If the RANGE is 'All real numbers', it means that the function can produce any value of y without restrictions.

Front

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

Back

An example is the function f(x) = x^2, which has a range of y ≥ 0, meaning it can only produce non-negative values.

Front

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

Back

An example is the function f(x) = 1/x, which has a domain of all real numbers except x = 0, since division by zero is undefined.

Front

What is the significance of identifying the DOMAIN and RANGE?

Back

Identifying the DOMAIN and RANGE helps in understanding the behavior of the function and in solving application-based problems.

Front

What is a continuous graph?

Back

A continuous graph is a graph that can be drawn without lifting the pencil from the paper, meaning it has no breaks, holes, or gaps.