Domain and Range from a Graph
Finding domain and range from a graph in Algebra 1 (California Reveal Math, Grade 9) means reading the graph's horizontal extent for domain (all x-values covered) and vertical extent for range (all y-values covered). For a continuous function graphed on a coordinate plane, the domain is the set of all x-values where the graph exists and the range is all corresponding y-values. Arrows indicate the graph continues to infinity. This skill is fundamental for understanding functions, their restrictions, and how they model real-world situations with natural limits.
Key Concepts
For a graph of a relation, the domain is the complete set of $x$ values the graph covers (its horizontal extent), and the range is the complete set of $y$ values the graph covers (its vertical extent).
$$\text{Domain} = \{x \mid x \text{ is covered by the graph left to right}\}$$ $$\text{Range} = \{y \mid y \text{ is covered by the graph bottom to top}\}$$.
Common Questions
How do you find the domain of a function from its graph?
Look at the horizontal span of the graph. The domain is all x-values for which the graph exists. Read from the leftmost to rightmost points (or to infinity if arrows extend).
How do you find the range of a function from its graph?
Look at the vertical span of the graph. The range is all y-values the graph reaches. Read from the lowest to highest points (or to infinity if arrows extend).
What do arrows on a graph mean for domain and range?
Arrows indicate the graph continues to infinity in that direction. A left arrow means the domain extends to -∞; a right arrow means to +∞. Up/down arrows mean range extends to ±∞.
What is interval notation for domain and range?
Interval notation uses brackets (inclusive) and parentheses (exclusive): [a, b] means a ≤ x ≤ b, (a, b) means a < x < b. Use ∞ with parentheses since infinity is never reached.
Where is reading domain and range from a graph covered in California Reveal Math Algebra 1?
This skill is taught in California Reveal Math, Algebra 1, as part of Grade 9 functions and their properties.
What is the difference between domain and range?
Domain is the set of all valid inputs (x-values). Range is the set of all resulting outputs (y-values) when the function is applied to every input in the domain.
What common mistakes do students make reading domain and range?
Students sometimes switch domain (x) and range (y), or miss endpoints (not checking whether dots are open or closed circles indicating included or excluded values).