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The graph shows a triangular shape, which is indicative of a **probability density function (pdf)**. A pdf describes the likelihood of a random variable falling within a certain range, and the area under the curve must be equal to 1. The reason this is a pdf and not a cumulative distribution function (cdf) is because the cdf would be non-decreasing and the curve of the function would not return to the horizontal axis like this graph does.

### To find the value of \( c \):
We need to use the property of the probability density function that the total area under the curve must equal 1.

The triangle is located between \( x = 2 \) and \( x = 4 \) on the x-axis. The base of the triangle is \( 4 - 2 = 2 \), and the height of the triangle is \( c \).

The area \( A \) of a triangle is given by the formula:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]

Substituting the known values:
\[
1 = \frac{1}{2} \times 2 \times c
\]

Simplifying this:
\[
1 = c
\]

Thus, the value of \( c \) must be **1**.

### Key points:
- The function is a **density function (pdf)**.
- The value of \( c \) is **1**.

Would you like any further details or explanations?

### Related Questions:
1. What is the difference between a probability density function (pdf) and a cumulative distribution function (cdf)?
2. How do you calculate the area under different types of pdfs (e.g., piecewise functions)?
3. How is the concept of a pdf related to the total probability rule?
4. Can the value of a pdf be greater than 1, and if so, under what conditions?
5. How do you interpret the probability for specific intervals based on this graph?

### Tip:
Always verify that the total area under a pdf equals 1 to ensure that the function represents a valid probability distribution.

What type of function is shown in the graph? What value must c have?

Learn how to determine the constant c for a triangular probability density function. This problem explores core probability concepts, including the area of a triangle and the rule that the total area under a probability density function must equal 1.

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