Question

What are the transformations on the graph of f(x)=1x
𝑓
(
𝑥
)
=
1
𝑥
if it is replaced by k(x)=−34x
𝑘
(
𝑥
)
=
−
3
4
𝑥
?(1 point)
Responses

It horizontally stretches by a factor of 43
4
3
and reflects across the y-axis.
It horizontally stretches by a factor of Start Fraction 4 over 3 End Fraction and reflects across the y -axis.

It vertically shifts up 34
3
4
units and reflects across the x-axis.
It vertically shifts up Start Fraction 3 over 4 End Fraction units and reflects across the x -axis.

It vertically stretches by a factor of 43
4
3
and reflects across the x-axis.
It vertically stretches by a factor of Start Fraction 4 over 3 End Fraction and reflects across the x -axis.

It vertically compresses by a factor of 34
3
4
and reflects across the x-axis.

Answer 1

To analyze the transformation from \( f(x) = \frac{1}{x} \) to \( k(x) = -\frac{3}{4} x \), we can break down the changes:

1. **From \( \frac{1}{x} \) to \( -\frac{3}{4} x \)**:
- The negative sign indicates a reflection across the x-axis.
- The coefficient of \(-\frac{3}{4}\) indicates a vertical compression by a factor of \( \frac{4}{3} \) since the absolute value of the coefficient is less than 1.

2. **No horizontal stretching or shifting** is present since there are no changes in \(x\) involving multiplication or addition (like \(x/a\) or \(x + b\)).

### Conclusion:
The correct transformation is that it vertically compresses by a factor of \( \frac{3}{4} \) and reflects across the x-axis.

**So the correct response is:**
"It vertically compresses by a factor of \( \frac{3}{4} \) and reflects across the x-axis."