Make a table listing ordered pairs for each function. Then...

Make a table listing ordered pairs for each function. Then sketch the graph and state the domain and range. Identify any intervals on which $f$ is increasing, decreasing, or constant.
$$f(x)=|x-1|$$

Key Concepts

Increasing/Decreasing Intervals

Analyzing the intervals where a function is increasing, decreasing, or constant involves examining how the output values change as the input values move along the domain. Understanding these intervals provides insight into the function’s behavior, such as where it attains its minimum or maximum values, and reveals trends in its rate of change.

Graphing Functions

Graphing a function is the process of plotting the computed ordered pairs on a coordinate plane and connecting them in an appropriate manner to depict the relationship between the variables. For absolute value functions, the graph typically forms a distinct V-shape, which helps in visualizing the function's symmetry and vertex.

Domain and Range

The domain of a function refers to the set of all possible input values for which the function is defined, while the range is the set of all possible outputs. For absolute value functions, the domain usually encompasses all real numbers and the range is limited to non-negative values, reflecting the nature of absolute value outputs.

Absolute Value Function

An absolute value function takes the input, usually represented as x, and returns its non-negative value. In essence, the function outputs the magnitude of the difference between x and a constant, which results in a V-shaped graph. This transformation ensures that regardless of whether the input within the function is positive or negative, the output remains non-negative.

Table of Values

Creating a table of values involves selecting input values from the domain of the function, computing the corresponding output using the function’s rule, and listing these ordered pairs. This technique aids in understanding the behavior and pattern of the function, providing a set of reference points for graphing.

Transcript

Please give Ace some feedback