Question

cubic & cube root functions unit online practice
complete this assessment to review what youve learned. it will not count toward your grade
what is one effect of replacing $f(x)$ with $f(bx)$ in the function $f(x)=x^3$ when $b < 0$? (1 point)
\bigcirc a reflection about the line $y = x$
\bigcirc a shift to the right
\bigcirc a shift to the left
\bigcirc a reflection about the $y$-axis

Explanation:

To determine the effect of replacing \( f(x) = x^3 \) with \( f(bx) \) when \( b < 0 \), we analyze function transformations. For a function \( y = f(x) \), replacing \( x \) with \( bx \) (horizontal scaling/reflection) has the rule: if \( b < 0 \), it introduces a reflection about the \( y \)-axis (since \( f(bx)=f(-|b|x) \), and reflecting \( f(x) \) over the \( y \)-axis gives \( f(-x) \)).

• A reflection about \( y = x \) is for inverse functions (not related to \( f(bx) \) here).
• Shifts (left/right) are caused by \( f(x \pm h) \), not \( f(bx) \).

Thus, the effect is a reflection about the \( y \)-axis.

Answer:

D. a reflection about the \( y \)-axis (Note: Assuming the last option is labeled as D; if original options have labels like the first option as A, adjust to the correct label with text. From the options, the last one is "a reflection about the \( y \)-axis", so the answer is the option with text "a reflection about the \( y \)-axis" (identify by its text and position as the fourth option, e.g., if options are A, B, C, D: D. a reflection about the \( y \)-axis).)