Problem 115 - Precalculus Essentials

Question

Explain how to identify the domain and range of a function from its graph.

Step-by-Step Solution

Answer

The domain of a function from its graph is the set of all x values, and it is identified by finding the lowest and highest x values where the graph exists. The range of a function from its graph is the set of all y values, and it is identified by finding the lowest and highest y values where the graph exists. These are expressed as an interval or a set, often using interval notation.

Step 1: Understand the definitions

The domain of a function is the set of all possible input values (often represented by x), which are allowed for the function. The range of a function is the set of output values (often represented by y), which result from the input values in the domain.

Step 2: Identify the Domain from the Graph

Take a look at the function's graph and identify the lowest and highest x-values where the graph exists. If the graph goes left or right indefinitely, the domain will be all real numbers. If not, the domain can be expressed as an interval from the lowest to the highest x-value.

Step 3: Identify the Range from the Graph

Now identify the lowest and highest y-values where the graph exists. If the graph goes up or down indefinitely, the range is all real numbers. If not, the range can be expressed as an interval from the lowest to the highest y-value.

Step 4: Express the Domain and Range

Finally, express the domain and range as an interval or a set. Domain and Range are often written in interval notation, where parentheses indicate that the endpoint is not included and square brackets indicate the endpoint is included. For example, [2,5) would represent that the domain or range starts at 2 and goes up to but does not include 5.