Question

1. which shifts $f(x) = \frac{1}{x}$ up by 3 units?

$\bigcirc$ $f(x) = \frac{1}{x} - 3$
$\bigcirc$ $f(x) = \frac{-1}{x + 3}$
$\bigcirc$ $f(x) = \frac{1}{x} + 3$
$\bigcirc$ $f(x) = \frac{1}{x - 3}$

Explanation:

Step1: Recall vertical shift rule

A vertical shift up by \(k\) units transforms \(f(x)\) to \(f(x) + k\).

Step2: Apply the rule

Here, \(k = 3\), so the transformed function is \(\frac{1}{x} + 3\).

Answer:

f(x) = \(\frac{1}{x}\) + 3