consider the graph of the function below.
a. identify the independent and dependent variables, and describe the domain and range.
b. describe the function in words.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Independent and Dependent Variables" ], "new_concepts": [], "current_concepts": [ "Independent and Dependent Variables", "Domain and Range", "Graph Interpretation" ] } ## Identify variables from graph axes Using the *Independent and Dependent Variables* knowledge point $$ \begin{aligned} &\text{Horizontal Axis (x-axis)} = \text{Year} \implies \text{Independent Variable}\ &\text{Vertical Axis (y-axis)} = \text{World population (in billions)} \implies \text{Dependent Variable} \end{aligned} $$ ## Determine domain and range Using the *Domain and Range* knowledge point $$ \begin{aligned} &\text{Domain (input values on horizontal axis): } [1950, 2000]\ &\text{Range (output values on vertical axis): } [2.2, 5.7] \end{aligned} $$ ## Describe the function in words Using the *Graph Interpretation* knowledge point $$ \begin{aligned} &\text{The graph shows how world population (in billions) changed over time from 1950 to 2000.}\ &\text{The population increased steadily from approximately 2.2 billion in 1950 to about 5.7 billion in 2000.} \end{aligned} $$ a. The independent variable is the year and the dependent variable is the population. The domain is the set of years from 1950 to 2000, which can be written as $[1950, 2000]$. The range is the set of population values from approximately 2.2 billion to 5.7 billion, which can be written as $[2.2, 5.7]$ billion. b. In words, the function describes how the world population changed over time from the year 1950 to 2000. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Independent and Dependent Variables" ] }

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Identify variables from graph axes

Determine domain and range

Describe the function in words

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