Select the correct row in the table. Which row of the table reveals the $y$-intercept of function $f$?
| x | f(x) |
| --- | ------------- |
| -1 | $2 \frac{2}{3}$ |
| 0 | 2 |
| 1 | 0 |
| 2 | -6 |
| 3 | -24 |
Answer (2)
The y -intercept occurs when x = 0 .
Identify the row in the table where x = 0 .
The corresponding f ( x ) value is the y -intercept.
The y -intercept is 2 .
Explanation
Finding the y-intercept The y -intercept of a function is the point where the graph of the function intersects the y -axis. This occurs when x = 0 . We need to find the row in the table where x = 0 .
Identifying the y-intercept from the table Looking at the table, we see that when x = 0 , f ( x ) = 2 . Therefore, the y -intercept is 2.
Conclusion The row that reveals the y -intercept of function f is the row where x = 0 and f ( x ) = 2 .
Examples
Understanding the y-intercept is crucial in many real-world applications. For example, in a linear cost function y = m x + b , where y is the total cost and x is the number of units produced, b represents the fixed cost (the cost when no units are produced, i.e., x = 0 ). Knowing the y-intercept helps businesses understand their initial investment before production begins. Similarly, in physics, if you graph the velocity of an object over time, the y-intercept represents the initial velocity of the object at time t = 0 .
The y -intercept occurs at x = 0 . In the table, when x = 0 , the corresponding value of f ( x ) is 2 , which means the y -intercept is 2. Thus, the correct row in the table is the one where x = 0 .
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