The graph of \( k(x)=x^{3}-4 \) needs to be horizontally stretched by a factor of 3 . What should the value of \( b \) be in the new function \( h(x)=(b x)^{3}-4 \) ? If your response is not a whole number, enter it as a fraction. (1 point)

To horizontally stretch the function \( k(x) = x^{3} - 4 \) by a factor of 3, we substitute \( x \) with \( \frac{x}{3} \) in the function. Therefore, the new function becomes \( k\left(\frac{x}{3}\right) = \left(\frac{x}{3}\right)^{3} - 4 \). This can be represented as \( h(x) = b x^{3} - 4 \) where \( b \) needs to be determined. From the substitution, we see that \( h(x) = k\left(\frac{x}{3}\right) \) leads to \( h(x) = \frac{1}{27}x^{3} - 4 \). Thus, in the form \( h(x) = (b x)^{3} - 4 \), we identify \( b \) as \( \frac{1}{3} \). So, the value of \( b \) is \( \frac{1}{3} \).