Graph of a function

Definition

A graph of a function is a visual representation of all the ordered pairs $(x, y)$ that satisfy the function $y = f(x)$. It helps in understanding the behavior and properties of the function.

5 Must Know Facts For Your Next Test

1. The graph of a function can be used to identify its domain and range.
2. Critical points such as intercepts, maxima, minima, and inflection points are easily observed on the graph.
3. Vertical line test can determine if a graph represents a function; if any vertical line intersects the graph more than once, it is not a function.
4. Asymptotes, both horizontal and vertical, can be identified from the graph for functions with undefined values or behavior at infinity.
5. Transformation of functions, including translations, reflections, stretches, and compressions, affect their graphs accordingly.

Review Questions

• How do you determine if a graph represents a function using the vertical line test?
• What information can you derive about a function's domain and range by analyzing its graph?
• Explain how transformations such as translations or reflections affect the graph of a given function.

Related terms

Domain: The set of all possible input values (x-values) for which the function is defined.

Range: The set of all possible output values (y-values) produced by the function.

Asymptote: A line that the graph of a function approaches but never touches as it heads towards infinity.