Question

1. in which direction is the graph of $f(x) = \frac{6}{x + b}$ translated when $b$ increases?

a left
b right
c up
d down

Explanation:

Step1: Recall rational function shifts

The parent function is $g(x)=\frac{5}{x}$. For a transformed function $f(x)=\frac{5}{x + b}$, horizontal shifts follow: $x + b = x - (-b)$.

Step2: Analyze shift direction

When $b$ increases, $-b$ becomes a larger negative value. A horizontal shift of $g(x)$ by $h$ units right is $g(x - h)$. Here, $h = -b$, so increasing $b$ makes $h$ more negative, which shifts the graph left.

Answer:

A. left