Question

reflecting the cubic function quick check
analyze the effect on the domain of $f(x) = x^3$ when $f(x)$ is replaced by $f(bx)$ with $b < 0$. (1 point)

• the domain changes to zero.
• the domain changes to all negative real numbers.
• the domain remains all real numbers.
• the domain remains all positive real numbers.

Explanation:

The original function \( f(x) = x^3 \) has a domain of all real numbers because any real number can be cubed. When we replace \( x \) with \( bx \) (where \( b < 0 \)), we are looking at \( f(bx)=(bx)^3 \). For any real number \( x \), \( bx \) is still a real number (since \( b \) is a real number and multiplying a real number by another real number gives a real number), and cubing a real number is defined for all real numbers. So the domain remains all real numbers.

Answer:

The domain remains all real numbers.