Graphing the Function y = f(x) = 2x
To graph the function y = f(x) = 2x for the range of x from 1 to 4, follow these steps:
Step 1: Identify the Values of x
We will be focusing on the values: x = 1, x = 2, x = 3, and x = 4.
Step 2: Calculate Corresponding y Values
Now, let’s calculate y for each x:
- For x = 1:
y = 2 * 1 = 2 - For x = 2:
y = 2 * 2 = 4 - For x = 3:
y = 2 * 3 = 6 - For x = 4:
y = 2 * 4 = 8
Step 3: Plot the Points
Now, plot the points on a graph:
- (1, 2)
- (2, 4)
- (3, 6)
- (4, 8)
Step 4: Draw the Line
After plotting the points, draw a straight line through them. This line represents the function y = 2x.
Step 5: Analyze the Graph
The graph of the function y = 2x is a straight line with a slope of 2, starting from the origin and passing through the points calculated above. As x increases, y also increases proportionally, demonstrating the function’s linear relationship. The graph between x = 1 and x = 4 provides a clear visualization of how this function behaves over the specified interval.
Conclusion
Graphing helps you understand the behavior of functions! The line you draw for y = 2x clearly shows a direct correlation between x and y, making it easy to see how changes in x impact y.