Analyze the effect on the graph of f(x)=lnx

Question

when f(x)
is replaced by −17f(x)
.(1 point)
Responses

The graph reflects across the y-axis and vertically stretches by a factor of 7.
The graph reflects across the y -axis and vertically stretches by a factor of 7.

The graph reflects across the x-axis and vertically stretches by a factor of 7.
The graph reflects across the x -axis and vertically stretches by a factor of 7.

The graph reflects across the x-axis and vertically compresses by a factor of 17
.
The graph reflects across the x -axis and vertically compresses by a factor of Start Fraction 1 over 7 End Fraction .

The graph reflects across the y-axis and vertically compresses by a factor of 17
.
The graph reflects across the y -axis and vertically compresses by a factor of Start Fraction 1 over 7 End Fraction .

Answer 1

To analyze the effect on the graph of the function \( f(x) = \ln(x) \) when it is replaced by \( -17f(x) \), we can break down the transformations involved:

1. Negative sign (-): Replacing \( f(x) \) with \( -f(x) \) reflects the graph across the x-axis.

2. Multiplier (17): When multiplying \( f(x) \) by 17, \( 17f(x) \) vertically stretches the graph by a factor of 17. Since we have a negative sign in front, we need to consider that in combination with the vertical stretch.

Putting these transformations together:

• The function \( -17f(x) \) reflects the graph across the x-axis (due to the negative sign) and vertically stretches it by a factor of 17 (because of the 17).

Thus, the correct response is:

The graph reflects across the x-axis and vertically stretches by a factor of 17.