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)
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)
Answers
GPT-4o mini
To understand the effect on the graph of the function \( f(x) = x \) when it is replaced by \( g(x) = \frac{1}{12} x \), we need to analyze how the transformation affects the graph.
1. **Original function:** \( f(x) = x \) is a linear function with a slope of 1.
2. **Transformed function:** \( g(x) = \frac{1}{12} x \) has a slope of \( \frac{1}{12} \).
This change from \( x \) to \( \frac{1}{12} x \) indicates that the graph is being vertically compressed because the coefficient multiplying \( x \) is less than 1.
Thus, the correct option is:
**Option #1: vertically compressed by a factor of \( \frac{1}{12} \)**.
Therefore, the answer is that the graph is vertically compressed by a factor of \( 12 \).
1. **Original function:** \( f(x) = x \) is a linear function with a slope of 1.
2. **Transformed function:** \( g(x) = \frac{1}{12} x \) has a slope of \( \frac{1}{12} \).
This change from \( x \) to \( \frac{1}{12} x \) indicates that the graph is being vertically compressed because the coefficient multiplying \( x \) is less than 1.
Thus, the correct option is:
**Option #1: vertically compressed by a factor of \( \frac{1}{12} \)**.
Therefore, the answer is that the graph is vertically compressed by a factor of \( 12 \).