Question

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

Answer 1

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**