Question

function g is a transformation of function f using a horizontal shift 3 units left and vertical compression by a factor of 1/2 . plot the corresponding point on function g. ​

Answer 1

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Answer:

  g(x) = x + 1

Step-by-step 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.