Math Problem Statement

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Mr. Richard asked his students for the domain of the exponential function shown in the graph. What will be the correct response? A. 1 < x < 6 B. 1 ≤ x < 8 C. 0 ≤ x < 8 D. 0 < x < 6

Solution

The graph shows an exponential function segment on a coordinate plane. Observing the range of xx-values on the graph, we can see that xx starts just above 0 and goes up to, but does not include, 8. Therefore, the correct domain of the function is:

C. 0x<80 \leq x < 8

Would you like more details on how to interpret domains for graphs?

Here are 5 related questions for further exploration:

  1. How do you determine the range of an exponential function?
  2. Why is the domain of this exponential function restricted to specific values?
  3. What are some general properties of exponential functions?
  4. How would you find the asymptote of this function?
  5. What is the significance of open and closed intervals in domains?

Tip: When determining domains, pay attention to endpoints on the graph—whether they are included (closed circle) or excluded (open circle).

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Math Problem Analysis

Mathematical Concepts

Exponential Functions
Domain of Functions
Inequalities

Formulas

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Theorems

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Suitable Grade Level

Grades 9-10