Question

The graph of the function f(x)=1x
is vertically compressed by a factor of 111
. Which of the following is the expression representing the new graph of the function?(1 point)
Responses

g(x)=1x+11
g left parenthesis x right parenthesis equals Start Fraction 1 over x plus 11 End Fraction

g(x)=111x
g left parenthesis x right parenthesis equals Start Fraction 1 over 11 x End Fraction

g(x)=1x−11
g left parenthesis x right parenthesis equals Start Fraction 1 over x End Fraction minus 11

g(x)=11x

Answer 1

A vertical compression of a graph by a factor of \( k \) means that the \( y \)-values of the function are multiplied by \( 1/k \). In this case, the original function is \( f(x) = \frac{1}{x} \). To vertically compress it by a factor of \( 111 \), we multiply the function by \( \frac{1}{111} \).

So, the new function \( g(x) \) would be:

\[
g(x) = \frac{1}{111} \cdot \frac{1}{x} = \frac{1}{11x}
\]

Thus, the correct expression representing the new graph of the function is:

\[
g(x) = \frac{1}{11x}
\]

This corresponds to the option:

**g left parenthesis x right parenthesis equals Start Fraction 1 over 11 x End Fraction**.