The graph of a function f is given: Use the graph to answer the question Use the graph of f given below to find f(20). ~25
The Correct Answer and Explanation is:
Correct Answer:
f(20) = 15
Explanation:
To find the value of a function, such as f(20), from its graph, we need to determine the output value (the y-coordinate) that corresponds to the given input value (the x-coordinate). The graph visually represents the set of all points (x, f(x)).
Step 1: Understand the Graph’s Scale
First, we must interpret the scale of the coordinate axes. The horizontal x-axis and the vertical y-axis are labeled with values like 25 and -25. By observing the tick marks between the origin (0,0) and the label ’25’ on both axes, we can see there are five intervals. This means each tick mark represents a step of 25 ÷ 5 = 5 units. So, along the x-axis, the tick marks to the right of the origin represent x = 5, 10, 15, 20, 25, and so on. Similarly, the tick marks above the origin on the y-axis represent y = 5, 10, 15, 20, 25.
Step 2: Locate the Input Value on the Horizontal Axis (x-axis)
The question asks for f(20). This means our input value is x = 20. We locate this value on the x-axis by starting at the origin and moving to the right. The fourth tick mark from the origin corresponds to x = 20.
Step 3: Find the Corresponding Point on the Graph of the Function
From the position x = 20 on the x-axis, we trace a vertical line upwards until it intersects the curve of the function f. The graph has a distinct point plotted at this x-value.
Step 4: Determine the Output Value from the Vertical Axis (y-axis)
Once we have identified the point on the curve at x = 20, we trace a horizontal line from this point over to the y-axis to read its corresponding y-value. This horizontal line aligns with the third tick mark above the origin on the y-axis.
Conclusion
Since each tick mark on the y-axis represents 5 units, the third tick mark corresponds to a value of 3 × 5 = 15. Therefore, the point on the graph is (20, 15). By definition, f(x) = y, so we can conclude that f(20) = 15.thumb_upthumb_down
