Questions: Give the domain and the range of the function in the graph. How can the graph of a function be used to determine the domain of the function? A. Find all points on the horizontal axis through which a vertical line meets the graph. B. Find all points on the vertical axis through which a horizontal line meets the graph. C. Find the highest and lowest points on the graph. The domain will be all x-values between these points. D. Find all points where the graph crosses the x-axis.

Solution Steps

To determine the domain of a function from its graph, you need to identify all the possible $x$-values for which the function is defined. This can be done by observing the horizontal extent of the graph.

1. Look at the graph and identify the leftmost and rightmost points where the graph exists.
2. The domain will be all $x$-values between these points, inclusive if the points are included in the graph.

To determine the domain of the function, we need to find the range of \( x \)-values for which the function is defined. By examining the given points \((-3, 2)\), \((-1, 4)\), \((0, 5)\), \((2, 3)\), and \((4, 1)\), we can see that the smallest \( x \)-value is \(-3\) and the largest \( x \)-value is \(4\).

The domain of the function is the interval from the smallest \( x \)-value to the largest \( x \)-value. Therefore, the domain is: \[ \text{Domain} = [-3, 4] \]

To determine the domain of a function from its graph, we need to find all points on the horizontal axis through which a vertical line meets the graph. This corresponds to option A.

Final Answer