Analyze the effect on the domain of \( f(x)=x^{3} \), when \( f(x) \) is replaced by \( f(b x) \) with \( b<0 \). (1 point) The domain remains all real numbers. The domain changes to zero. The domain changes to all negative real numbers. The domain remains all positive real numbers.

When you replace \( f(x) = x^3 \) with \( f(bx) \) where \( b < 0 \), the function becomes: \[ f(bx) = (bx)^3 = b^3 x^3 \] The domain of the original function \( f(x) = x^3 \) is all real numbers (\( \mathbb{R} \)). Replacing \( x \) with \( bx \) does not impose any new restrictions on \( x \). The cube function is defined for all real numbers, regardless of the scaling factor \( b \), even if \( b \) is negative. **Answer:** The domain remains all real numbers.