Question
What is the effect on the graph of f(x)=1x when it is replaced by the function k(x)=98x ?(1 point) Responses It is vertically compressed by a factor of 98 . It is vertically compressed by a factor of Start Fraction 9 over 8 End Fraction . It is vertically compressed by a factor of 8. It is vertically compressed by a factor of 8. It is vertically stretched by a factor of 98 . It is vertically stretched by a factor of Start Fraction 9 over 8 End Fraction . It is vertically stretched by a factor of 9.
Answers
GPT-4o mini
To determine the effect on the graph of the function \( f(x) = 1x \) when it is replaced by \( k(x) = 98x \), we need to compare the two functions.
1. The function \( f(x) = 1x \) is a linear function with a slope of 1.
2. The function \( k(x) = 98x \) has a slope of 98.
When scaling the slope from 1 to 98, the graph of \( f(x) \) is affected in the following way:
- Since the slope increases from 1 to 98, the graph becomes steeper. This indicates that it is a vertical stretch.
Now, to determine the factor by which it is stretched:
- The factor of stretching can be found by comparing the new slope (98) to the original slope (1). Since the slope is multiplied by 98, we say that the function is vertically stretched by a factor of 98.
Thus, the correct response is:
**It is vertically stretched by a factor of 98.**
1. The function \( f(x) = 1x \) is a linear function with a slope of 1.
2. The function \( k(x) = 98x \) has a slope of 98.
When scaling the slope from 1 to 98, the graph of \( f(x) \) is affected in the following way:
- Since the slope increases from 1 to 98, the graph becomes steeper. This indicates that it is a vertical stretch.
Now, to determine the factor by which it is stretched:
- The factor of stretching can be found by comparing the new slope (98) to the original slope (1). Since the slope is multiplied by 98, we say that the function is vertically stretched by a factor of 98.
Thus, the correct response is:
**It is vertically stretched by a factor of 98.**