The = graph of a function f is given: Use the graph to answer the question Use the graph of f given below to find ((50), 100
The Correct Answer and Explanation is:
Understanding the Graph of a Function
To find the value of a function, such as f(x), from its graph, we need to interpret the relationship between the coordinate axes and the function’s curve. The horizontal axis, commonly known as the x-axis, represents the input values for the function. The vertical axis, or y-axis, represents the corresponding output values. The curve drawn on the plane illustrates the specific output value (y-coordinate) for every given input value (x-coordinate).
The notation f(50) asks for the specific output value of the function ‘f’ when the input value ‘x’ is 50.
Step-by-Step Solution
- Identify the Input Value: The expression we need to evaluate is f(50). In this notation, the number inside the parentheses, 50, is our input value. This corresponds to a specific location on the x-axis.
- Locate the Input on the x-axis: We start by finding the number 50 on the horizontal x-axis. The graph has markings, and the value “50” is explicitly labeled to the right of the origin (0,0).
- Find the Corresponding Point on the Graph: From the position x = 50 on the x-axis, we trace a vertical line up or down until we intersect the curve that represents the function f. As we look at the graph, we can see that at the exact point where x = 50, the function’s curve crosses the x-axis.
- Determine the Output Value from the y-axis: Once we have located the point on the curve, we must determine its corresponding y-value. We do this by tracing a horizontal line from that point over to the y-axis. Since the point for x = 50 lies directly on the x-axis, its vertical distance from the x-axis is zero. Therefore, its y-coordinate is 0.
Conclusion
The point on the graph corresponding to the input x = 50 is (50, 0). Since the y-value represents the output of the function, we can conclude that f(50) = 0.
Comparing this result with the given choices:
A) 0
B) 60
C) 100
D) 50
The correct option is A.
The correct answer is A) 0.
