Question

Circle the correct descritions for each equation
Descritions:
Is the input or output affected
Vertical Effect or Horizontal Effect
Stretch or Compression
Equations:
1.) y = root(3)(x)
2.) y = 1/3 x^2
3.) y = |1/2x|
4.) y = root(3)(10x)
5.) y = 4*2^x

Answer 1

Let's analyze each equation to determine the effects on input or output, whether it's vertical or horizontal, and whether it represents a stretch or compression.

### 1.) \( y = \sqrt{3}(x) \)
- **Is the input or output affected?**: Output
- **Vertical Effect or Horizontal Effect**: Vertical Effect
- **Stretch or Compression**: Stretch (since \(\sqrt{3} > 1\))

### 2.) \( y = \frac{1}{3} x^2 \)
- **Is the input or output affected?**: Output
- **Vertical Effect or Horizontal Effect**: Vertical Effect
- **Stretch or Compression**: Compression (since \(0 < \frac{1}{3} < 1\))

### 3.) \( y = | \frac{1}{2}x | \)
- **Is the input or output affected?**: Input
- **Vertical Effect or Horizontal Effect**: Horizontal Effect
- **Stretch or Compression**: Compression (because \(\frac{1}{2} < 1\))

### 4.) \( y = \sqrt{3}(10x) \)
- **Is the input or output affected?**: Input
- **Vertical Effect or Horizontal Effect**: Horizontal Effect
- **Stretch or Compression**: Compression (as \(10 > 1\); scaling by a factor of 10 compresses the input)

### 5.) \( y = 4 \cdot 2^x \)
- **Is the input or output affected?**: Output
- **Vertical Effect or Horizontal Effect**: Vertical Effect
- **Stretch or Compression**: Stretch (since \(4 > 1\))

### Summary
- **1.)** Output, Vertical Effect, Stretch
- **2.)** Output, Vertical Effect, Compression
- **3.)** Input, Horizontal Effect, Compression
- **4.)** Input, Horizontal Effect, Compression
- **5.)** Output, Vertical Effect, Stretch