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Let f(x)=-2x+4 Graph g(x)=f(x)-3

User Ajk
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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:

User Ahmed Kooli
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