What is the range of \[f\]?
A coordinate plane. The x- and y-axes both scale by one. The graph of the function f starts at negative six, three which is plotted. A line segment connects negative six, three to negative four, negative three. A line segment connects negative four, negative three to negative two, six. A line segment connects negative two, six to six, seven. which is plotted.
Choose 1 answer:
Choose 1 answer:
(Choice A)   The \[f(x)\]-values \[-3\], \[3\], \[6\], and \[7\]
A
The \[f(x)\]-values \[-3\], \[3\], \[6\], and \[7\]
(Choice B)   \[-6 \leq f(x) \leq 6\]
B
\[-6 \leq f(x) \leq 6\]
(Choice C)   \[-3 \leq f(x) \leq 7\]
C
\[-3 \leq f(x) \leq 7\]
(Choice D)   The \[f(x)\]-values \[-6\], \[-4\], \[-2\], and \[6\]
D
The \[f(x)\]-values \[-6\], \[-4\], \[-2\], and \[6\]

The range of a function is the set of all possible \(f(x)\) values (output values) that the function can take. 

Based on the description of the graph:
- The function \(f(x)\) passes through the points \((-6, 3)\), \((-4, -3)\), \((-2, 6)\), and \((6, 7)\).
- The \(y\)-values (or \(f(x)\) values) of these points are \(3\), \(-3\), \(6\), and \(7\).

To determine the range of the function:
- The smallest \(f(x)\) value is \(-3\).
- The largest \(f(x)\) value is \(7\).

So the range of \(f(x)\) is all values between \(-3\) and \(7\), inclusive. This matches with choice (C).

**Correct answer:**
- **(Choice C) \([-3 \leq f(x) \leq 7]\)**

Would you like more details, or do you have any questions?

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Here are some additional questions for practice:
1. What is the domain of \(f(x)\)?
2. How would the range change if the graph included the point \((8, 10)\)?
3. If \(f(x)\) were a quadratic function, how could you determine its range?
4. What is the difference between the range and the codomain of a function?
5. How can you find the range of a function given its equation instead of a graph?
6. What does it mean for a function to have an infinite range?
7. How does the range of a function relate to its maximum and minimum values?
8. How would you describe the range of a function that has a vertical asymptote?

**Tip:** Always remember to look for the highest and lowest points on a graph to determine the range of a function.

Learn how to determine the range of a function from a given graph with detailed explanations. This problem involves analyzing points on a coordinate plane and identifying the output values (\(f(x)\)) of the function. Suitable for Grades 7-9 students preparing for function analysis.

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