Question

excellence question (indicator rf2.2)

the function \\(y = f(x)\\) has a domain of \\(\\{x \mid -8 \le x \le 4, x \in \mathbb{r}\\}\\) and a range of \\(\\{y \mid -2 \le y \le 12, y \in \mathbb{r}\\}\\). if \\(g(x) = f(x - h) + k\\) has a domain of \\(\\{x \mid -3 \le x \le 9, x \in \mathbb{r}\\}\\) and a range of \\(\\{y \mid -7 \le y \le 7, y \in \mathbb{r}\\}\\), determine the values of \\(h\\) and \\(k\\).

Explanation:

Determine the horizontal shift \(h\)

Using the Horizontal Translation and Function Transformations knowledge points

$$
LATEXBLOCK0
$$

Determine the vertical shift \(k\)

Using the Vertical Translation and Function Transformations knowledge points

$$
LATEXBLOCK1
$$

Answer:

\(h = 5\) and \(k = -5\)