9514 1404 393
Answer:
g(x) = x + 1
Explanation:
The transformation "shift left 3 units" is accomplished by replacing x in the function definition by x+3.
F(x) is defined as ...
f(x) = 2x -4
Then the left shift gives ...
f(x +3) = 2(x +3) -4 = 2x +2
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The transformation "vertical compression by a factor of 1/2" is accomplished by multiplying the function by 1/2.
g(x) = 1/2f(x +3) = (1/2)(2x +2)
g(x) = x +1
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In the attached, we wanted to show where the table points would end up if they were shifted left 3, then moved half their vertical distance toward the x-axis (compression by 1/2). Doing that, the points in the first table become the points in the second table. This is different from what you get when you simply substitute the same values of x into the new function g.
Consider, for instance, the bottom left point on the red graph. When it is moved 3 left, its coordinates are (-3, -4). When the y-coordinate is cut in half, its new location is (-3, -2), the bottom left point on the blue graph.