how can i graph this piecewise function :
f(x) = {x-4, if x<1
3x, if x>1
To graph a piecewise function like f(x) = {x-4, if x<1; 3x, if x>1}, you will need to plot the different portions of the function separately based on their respective domains.
1. Identify the domains:
- For the first portion, x<1.
- For the second portion, x>1.
2. Plotting the first portion:
- For x values less than 1, substitute these values into the function f(x) = x-4.
- Choose some values for x that are less than 1, like x = -2, -1, 0.
- Calculate the corresponding y values by substituting these x values into the function.
For example, f(-2) = (-2) - 4 = -6.
- Plot the points (-2, -6), (-1, -5), and (0, -4) on the graph.
3. Plotting the second portion:
- For x values greater than 1, substitute these values into the function f(x) = 3x.
- Choose some values for x that are greater than 1, like x = 2, 3, 4.
- Calculate the corresponding y values by substituting these x values into the function.
For example, f(2) = 3(2) = 6.
- Plot the points (2, 6), (3, 9), and (4, 12) on the graph.
4. Connecting the points:
- Draw a solid line between the points related to the first portion, where x<1.
- Draw a solid line between the points related to the second portion, where x>1.
- Ensure that the lines do not connect between the two portions since the function has a gap at x=1.
Once you have plotted these points and connected the lines, you will have the graph of the piecewise function f(x) = {x-4, if x<1; 3x, if x>1}.