Question

the graph of $f(x) = \frac{1}{x}$ has been transformed to create the graph of $g(x) = \frac{1}{bx}$. what is the value of $b$? \
\
\bigcirc \\ 3 \
\bigcirc \\ -3 \
\bigcirc \\ \frac{1}{3} \
\bigcirc \\ -\frac{1}{3}

Explanation:

Step1: Pick a point on $g(x)$

From the graph, take the point $(1, -3)$ which lies on $g(x)$.

Step2: Substitute into $g(x)$ formula

Substitute $x=1$, $g(x)=-3$ into $g(x)=\frac{1}{bx}$:
$$-3 = \frac{1}{b(1)}$$

Step3: Solve for $b$

Rearrange to isolate $b$:
$$b = \frac{1}{-3} = -\frac{1}{3}$$

Answer:

• $\boldsymbol{-\frac{1}{3}}$ (corresponding to the last option)