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Step 1:I'll explain how to find the range of a graph step by step:
Step 2:: Understand the Definition of Range
The range of a graph is the set of all possible y-values (output values) that the function can produce. In other words, it represents all the vertical values that the graph touches on the y-axis.
Step 3:: Determine the Range by Examining the Graph
To find the range, you need to: - Look at the vertical extent of the graph - Identify the lowest and highest y-values the graph reaches - Consider whether the graph includes all y-values between these points
Step 4:: Different Methods for Finding Range
- Solve the equation $$y = f(x)$$ for x
Method A: Visual Inspection - Trace the graph vertically - Determine the minimum and maximum y-values - Consider if the graph includes all values between these points Method B: Algebraic Analysis - Determine the constraints on y - Identify the possible y-values
Step 5:: Common Range Scenarios
- Continuous function: Range might be all y-values between a minimum and maximum - Discrete function: Range might be specific, isolated y-values - Unbounded function: Range could be all real numbers or half of the real numbers
Step 6:: Notation
- Example 2: $$\{y \in \mathbb{R} : -3 \leq y \leq 3\}
Express the range using interval notation or set notation
Final Answer
Always carefully analyze the graph or function to determine its complete set of possible y-values.
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