Question

question 7 (5 points)
use a table of values to graph the function \\(f(x) = \sqrt{x} + 4\\). select the correct graph below.
a

Explanation:

Identify the parent function and its domain

Using the Function Transformations knowledge point

$$
LATEXBLOCK0
$$

Apply the vertical translation

Using the Vertical Translation knowledge point

$$
LATEXBLOCK1
$$

Create a table of key values

We select perfect square values for \(x\) to find integer coordinates:

• For \(x = 0\): \(f(0) = \sqrt{0} + 4 = 4 \implies (0, 4)\)
• For \(x = 1\): \(f(1) = \sqrt{1} + 4 = 5 \implies (1, 5)\)
• For \(x = 4\): \(f(4) = \sqrt{4} + 4 = 6 \implies (4, 6)\)
• For \(x = 9\): \(f(9) = \sqrt{9} + 4 = 7 \implies (9, 7)\)

Analyze the given option A

Let's check the graph shown in option A:

• The curve starts at the point \((4, 0)\).
• This corresponds to the function \(y = \sqrt{x - 4}\), not \(f(x) = \sqrt{x} + 4\).
• Therefore, option A is incorrect because it represents a horizontal shift to the right by 4 units instead of a vertical shift up by 4 units.

Determine the correct graph characteristics

The correct graph must:

• Start at \((0, 4)\) on the y-axis.
• Curve upwards and to the right, passing through \((4, 6)\) and \((9, 7)\).

Answer:

• (A) A curve starting at \((4, 0)\) and passing through \((8, 2)\)
• (B) A curve starting at \((0, 4)\) on the y-axis and passing through \((4, 6)\) and \((9, 7)\) (Correct answer)