Questions: What is the domain of the transformation y=f(x-7)+6? -13 ≤ x ≤ -3 -4 ≤ x ≤ 6 3 ≤ x ≤ 13 1 ≤ x ≤ 11 7 ≤ x ≤ 17

Transcript text: \[ f(x) \] (a) What is the domain of the transformation $y=f(x-7)+6$ ? $-13 \leq x \leq-3$ $-4 \leq x \leq 6$ $3 \leq x \leq 13$ $1 \leq x \leq 11$ $7 \leq x \leq 17$

Solution

Solution Steps

Step 1: Identify the original domain of $ f(x) $

The graph of $ f(x) $ shows that the function is defined from $ x = -4 $ to $ x = 6 $.

Step 2: Determine the effect of the transformation $ y = f(x - 7) + 6 $

The transformation $ y = f(x - 7) + 6 $ involves a horizontal shift to the right by 7 units and a vertical shift up by 6 units. The vertical shift does not affect the domain.

Step 3: Calculate the new domain after the horizontal shift

Since the original domain is $ -4 \leq x \leq 6 $, shifting this domain 7 units to the right results in the new domain: \[ -4 + 7 \leq x \leq 6 + 7 \] \[ 3 \leq x \leq 13 \]