Question

what transformation takes the graph of $f(x) = 2x + 3$ to the graph of $g(x) = 2x + 4$?

• translation 1 unit left
• translation 1 unit down
• translation 1 unit right
• translation 1 unit up

Explanation:

Step1: Rewrite $g(x)$ in terms of $f(x)$

$g(x) = 2x + 4 = (2x + 3) + 1 = f(x) + 1$

Step2: Identify vertical translation rule

For $g(x) = f(x) + k$, if $k>0$, shift up $k$ units. Here $k=1$, so shift up 1 unit.

Answer:

translation 1 unit up