The graph of \( g(x)=x^{3}+1 \) needs to be horizontally compressed by a factor of \( \frac{1}{12} \) What should the value of \( b \) be in the new function \( h(x)=(b x)^{3}+1 \) ? (1 point) \( \frac{1}{12} \) 12 \( -\frac{1}{12} \) -12

To horizontally compress the function \( g(x) = x^3 + 1 \) by a factor of \( \frac{1}{12} \), you need to replace \( x \) in the original function with \( \frac{x}{\frac{1}{12}} \) (or \( 12x \)). This leads to the new function form being \( h(x) = (12x)^3 + 1 \). Therefore, the value of \( b \) should be 12. Additionally, when dealing with transformations of functions, remember that a horizontal compression by a factor of \( k \) can be represented by multiplying the input \( x \) by \( \frac{1}{k} \). This means that if you're compressing by \( \frac{1}{12} \), you'd effectively be using a multiplication factor of 12 in the new function, which matches our earlier finding!