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Select true or false for each description below.

The graph of y=log3(x)
was transformed into the new function y=−4log3(x−1)
by performing the following transformations:

(1 point)
True False
Horizontal shift to the left 1 unit

Vertical shift down by 4 units

Vertical stretch by a factor of 4

Reflection across the y-axis

1 answer

Let's analyze the transformations applied to the function \( y = \log_3(x) \) to convert it into \( y = -4\log_3(x - 1) \).

  1. Horizontal shift to the left 1 unit: False

    • The transformation \( x - 1 \) indicates a horizontal shift to the right by 1 unit.

  2. Vertical shift down by 4 units: False

    • The transformation involves multiplying by -4 but does not include an addition or subtraction of a constant term, thus there is no vertical shift.

  3. Vertical stretch by a factor of 4: True

    • The function is multiplied by -4, which indicates a vertical stretch by a factor of 4.

  4. Reflection across the y-axis: False

    • The negative sign in front of the 4 indicates a reflection across the x-axis, not the y-axis.

So the answers are:

  • Horizontal shift to the left 1 unit: False
  • Vertical shift down by 4 units: False
  • Vertical stretch by a factor of 4: True
  • Reflection across the y-axis: False