Question
What is the effect on the graph of f(x)=1x when it is replaced by g(x)=1112x ? Option #1: vertically compressed by a factor of 112 Option #2: horizontally stretched by a factor of 12 Option #3: horizontally compressed by a factor of 112 Option #4: horizontally shifted left by 112 unit (1 point) Option #
Answers
GPT-4o mini
To analyze the effect on the graph when replacing \( f(x) = x \) with \( g(x) = \frac{11}{12}x \), we need to consider how the transformation affects the slope of a linear function.
1. **Original Function**: \( f(x) = x \) has a slope of 1.
2. **New Function**: \( g(x) = \frac{11}{12}x \) has a slope of \( \frac{11}{12} \).
The slope of the new function is less than that of the original function, which indicates that the function \( g(x) \) will be vertically compressed compared to \( f(x) \).
### Explanation:
- A vertical compression by a factor of \( k \) (where \( 0 < k < 1 \)) means the graph gets "squished" towards the x-axis.
- In the case of \( g(x) = \frac{11}{12}x \), the factor \( \frac{11}{12} \) compresses the graph's vertical distance from the x-axis less than that of the original line.
### Conclusion:
The correct option describing this transformation is:
- **Option #1**: Vertically compressed by a factor of \( \frac{11}{12} \).
Thus, the answer is **Option #1**.
1. **Original Function**: \( f(x) = x \) has a slope of 1.
2. **New Function**: \( g(x) = \frac{11}{12}x \) has a slope of \( \frac{11}{12} \).
The slope of the new function is less than that of the original function, which indicates that the function \( g(x) \) will be vertically compressed compared to \( f(x) \).
### Explanation:
- A vertical compression by a factor of \( k \) (where \( 0 < k < 1 \)) means the graph gets "squished" towards the x-axis.
- In the case of \( g(x) = \frac{11}{12}x \), the factor \( \frac{11}{12} \) compresses the graph's vertical distance from the x-axis less than that of the original line.
### Conclusion:
The correct option describing this transformation is:
- **Option #1**: Vertically compressed by a factor of \( \frac{11}{12} \).
Thus, the answer is **Option #1**.