Answer:To graph the function g(x)=f(x)-3, we need to follow a step-by-step process:
1. Start with the original function f(x)=-2x+4. This is a linear function, which means it represents a straight line on the graph.
2. To graph f(x), we can choose some x-values and substitute them into the function to find the corresponding y-values. Let's choose a few values for x and calculate the corresponding y-values:
When x = 0:
f(0) = -2(0) + 4 = 4
So, we have the point (0, 4).
When x = 1:
f(1) = -2(1) + 4 = 2
So, we have the point (1, 2).
When x = -1:
f(-1) = -2(-1) + 4 = 6
So, we have the point (-1, 6).
3. Plot the points (0, 4), (1, 2), and (-1, 6) on a coordinate plane. Connect these points with a straight line to obtain the graph of f(x)=-2x+4.
4. Now, let's graph the function g(x)=f(x)-3. To do this, we need to subtract 3 from the y-values of each point on the graph of f(x).
For the point (0, 4), subtracting 3 gives us the new point (0, 1).
For the point (1, 2), subtracting 3 gives us the new point (1, -1).
For the point (-1, 6), subtracting 3 gives us the new point (-1, 3).
5. Plot the new points (0, 1), (1, -1), and (-1, 3) on the same coordinate plane. Connect these points with a straight line to obtain the graph of g(x)=f(x)-3.
Overall, the graph of g(x)=f(x)-3 is obtained by shifting the graph of f(x) downward by 3 units.
Explanation: