Question

Which of the following correctly identifies the transformations undergone from f(x)=x to f(3x)-1/3= 3x-1/3
Compressed horizontally and shifted down
Reflected over the y-axis and shifted up
Stretched horizontally and shifted down
Reflected over the x-axis and shifted up

Answer 1

To analyze the transformation from \( f(x) = x \) to \( f(3x) - \frac{1}{3} = 3x - \frac{1}{3} \), let's break it down step by step.

1. **Starting function**: \( f(x) = x \)

2. **Transformation to \( f(3x) \)**:
- Replacing \( x \) with \( 3x \) compresses the graph horizontally by a factor of 3. This means that for any value of \( y \), you need \( x \) to be a third of what it was in the original function to produce the same \( y \) value.

3. **Transformation to \( f(3x) - \frac{1}{3} \)**:
- The expression \( f(3x) - \frac{1}{3} \) indicates a vertical shift downward by \( \frac{1}{3} \).

Putting it all together:
- The transformation from \( f(x) = x \) to \( f(3x) \) compresses the graph horizontally.
- The transformation from \( f(3x) \) to \( f(3x) - \frac{1}{3} \) shifts the graph down.

Thus, the correct answer is:
**Compressed horizontally and shifted down**.