Which inequality best represents the range of the function?

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Understand the Problem

The question is asking which inequality best represents the range of a function based on a provided graph, which displays an athlete's run measured in distance over time.

Answer

$0 \leq f(x) \leq 100$
Answer for screen readers

The correct inequality is $0 \leq f(x) \leq 100$.

Steps to Solve

  1. Observe the Graph Examine the graph to determine the maximum and minimum distances traveled by the athlete. The x-axis represents time (in seconds), while the y-axis represents distance (in yards).

  2. Identify Maximum Distance From the graph, observe that the athlete reaches a maximum distance of 100 yards when the time is approximately 14 seconds.

  3. Determine Minimum Distance The minimum distance starts from the origin (0, 0), indicating that the distance cannot be negative. Therefore, the minimum distance is 0 yards.

  4. Formulate the Inequality Based on the observations, the function's range can be expressed as: $$ 0 \leq f(x) \leq 100 $$

  5. Select the Correct Option Review the available choices and select the one matching the derived inequality.

The correct inequality is $0 \leq f(x) \leq 100$.

More Information

This inequality indicates that the function representing the athlete's run has a range starting from 0 yards (at the beginning of the run) to a maximum of 100 yards.

Tips

  • Ignoring the Graph's Scale: Make sure to correctly interpret the axes and their units.
  • Misreading Maximum Values: Double-check the highest point reached on the graph to avoid underestimating the maximum distance.
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