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Find the Domain of a Graphed Function Using Interval Notation
Mathematics
Grade 10 (High School)
Question Content
Write the domain of the function shown in the graph using interval notation. The graph is a curve with closed endpoints at x = -1 and x = 4.
Correct Answer
[-1, 4]
Detailed Solution Steps
1
Step 1: Identify the domain of a function, which is the set of all possible x-values that the function covers from the graph.
2
Step 2: Locate the leftmost point on the graph: it is a closed dot at x = -1, meaning -1 is included in the domain.
3
Step 3: Locate the rightmost point on the graph: it is a closed dot at x = 4, meaning 4 is included in the domain.
4
Step 4: Write the domain in interval notation. Use square brackets for included endpoints, so the domain is [-1, 4].
Knowledge Points Involved
1
Domain of a Function
The domain of a function is the complete set of all possible input values (x-values) for which the function is defined. For graphical functions, it is the range of x-values that the graph spans horizontally.
2
Interval Notation
A mathematical notation used to represent a set of real numbers. Square brackets [ ] are used when the endpoint is included in the set (corresponding to a closed dot on a graph), and parentheses ( ) are used when the endpoint is not included (corresponding to an open dot on a graph).
3
Reading Function Graphs
When analyzing a function's graph, closed endpoints (solid dots) indicate that the x-value at that point is part of the function's domain, while open endpoints (hollow dots) indicate the x-value is not part of the domain.
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