Question

find the required values of the function \\(y = 3\sqrt{x + 2} - 7\\).

value: 4

match the items.

a. \\((-2, -7)\\)
b. \\(-7\\)
c. \\(3\\)
d. \\(-2\\)

1. \\(a\\)
2. \\(k\\)
3. \\(h\\)
4. vertex

Explanation:

Identify the standard form parameters

Using the Function Transformations knowledge point

$$ y = a\sqrt{x - h} + k $$

$$ y = 3\sqrt{x + 2} - 7 = 3\sqrt{x - (-2)} + (-7) $$

$$ a = 3,\quad h = -2,\quad k = -7 $$

Determine the vertical stretch factor

Using the Vertical Stretch knowledge point

$$ a = 3 $$

Determine the horizontal shift parameter

Using the Function Transformations knowledge point

$$ h = -2 $$

Determine the vertical shift parameter

Using the Function Transformations knowledge point

$$ k = -7 $$

Determine the vertex coordinates

Using the Vertex of Radical Function knowledge point

$$ \text{Vertex} = (h, k) = (-2, -7) $$

Match items to values

$$
LATEXBLOCK0
$$

Answer:

1. c
2. b
3. h
4. a