Question

I need help with this

Answer 1

9514 1404 393

Answer:

1. vertical shrink by a factor of 1/3
2. shift right 2 units
3. shift down 4 units

Step-by-step explanation:

The transformations of interest here are ...

  g(x) = k·f(x) . . . . . vertically scale f(x) by a factor of k

  g(x) = f(x -h) . . . . shift f(x) right by h units

  g(x) = f(x) +k . . . . shift f(x) up by k units

__

Working left to right, the first factor we encounter is 1/3, multiplying the value that is cubed. This means the vertical scale factor of f(x) = x^3 is 1/3. A scale factor less than 1 represents a shrink, so ...

  transformation #1 = shrink by a factor of 1/3

The next number we encounter is -2 in the factor (x -2)^3. This means h=2 in f(x -h) = (x -2)^3. The horizontal shift right is 2 units:

  transformation #2 = right shift 2 units

Finally, we encounter the number -4. This means k=-4 in g(x)=f(x)+k. The up-shift is negative, so ...

  transformation #3 = shift down 4 units

__

The right- and down-shifts can be done in either order. Here, we have done them as we see them when scanning the equation left-to-right. The vertical scaling must be done before the down-shift, so that it does not affect the amount of down-shift.