Answer:
Explanation:
To graph \(g(x) = f(x) - 2\), where \(f(x) = 3x + 1\), you can start by graphing \(f(x)\) and then shifting it downward by 2 units to graph \(g(x)\). Here are the steps:
1. **Graph \(f(x)\)**:
Start by plotting the graph of \(f(x) = 3x + 1\). This is a linear function with a slope of 3 and a y-intercept of 1. You can start with two points to draw the line:
- When \(x = 0\), \(f(0) = 3(0) + 1 = 1\), so the point (0, 1) is on the graph.
- When \(x = 1\), \(f(1) = 3(1) + 1 = 4\), so the point (1, 4) is on the graph.
Plot these points and draw a straight line passing through them. This is the graph of \(f(x)\).
2. **Graph \(g(x)\)**:
Now, to graph \(g(x) = f(x) - 2\), you will shift the graph of \(f(x)\) downward by 2 units. This means that every point on the graph of \(f(x)\) will be shifted 2 units down to form the graph of \(g(x)\).
So, if you had a point \((a, b)\) on the graph of \(f(x)\), it will be shifted to \((a, b - 2)\) on the graph of \(g(x)\).
3. **Shift the Graph of \(f(x)\) Downward by 2 Units**:
- The point (0, 1) on the graph of \(f(x)\) will shift to (0, -1) on the graph of \(g(x)\).
- The point (1, 4) on the graph of \(f(x)\) will shift to (1, 2) on the graph of \(g(x)\).
4. **Draw the Graph of \(g(x)\)**:
Using the shifted points, draw the graph of \(g(x)\). It will be a parallel line to the graph of \(f(x)\) but located 2 units lower.
Your final graph represents \(g(x) = f(x) - 2\), where \(f(x) = 3x + 1\), and it will be a line parallel to the graph of \(f(x)\) but shifted downward by 2 units.