Differentiating Between Relations and Functions
Differentiate between relations and functions in Grade 9 algebra. Use the vertical line test and input-output analysis to determine if each x-value maps to exactly one y-value.
Key Concepts
New Concept A function is a mathematical relationship pairing each value in the domain with exactly one value in the range.
In a function, the dependent variable $y$ is a function of the independent variable $x$. In terms of the variables, $y$ is a function of $x$ and can be written like the following example: $$y = f(x)$$ $$y = 5x + 2$$ $$f(x) = 5x + 2$$ What’s next Next, you’ll master the basics: identifying functions with the vertical line test, finding their domain and range, and writing your own function rules.
Common Questions
What is the difference between a relation and a function?
A relation is any set of ordered pairs. A function is a special relation where each input (x-value) has exactly one output (y-value). Every function is a relation, but not every relation is a function.
What is the vertical line test?
Draw vertical lines across the graph. If any vertical line crosses the graph more than once, it is NOT a function. If every vertical line touches at most once, it IS a function.
How do you identify a function from ordered pairs?
Check if any x-value repeats with different y-values. If each x-value appears with only one y-value, the set is a function.