Question

in the given function, the value of \\(k = 0\\).

since \\(2 > 0\\), the graph of the parent function is shifted 2 units right, and the vertex of the function is at \\((2, 0)\\).

activity

value: 1

which statement is true for the graph of the function \\(y = \sqrt{x + 5}\\)?

a. shift the parent graph 5 units to the right.
b. shift the parent graph 5 units to the left.
c. shift the parent graph 5 units upward.
d. shift the parent graph 5 units downward.

Explanation:

Identify the parent function and the transformation

The parent function is \(y = \sqrt{x}\). The given transformed function is:

$$y = \sqrt{x + 5}$$

Apply horizontal translation rule

A horizontal shift of a parent function \(f(x)\) is represented by \(f(x - h)\):

• If \(h > 0\), the graph shifts right by \(h\) units.
• If \(h < 0\), the graph shifts left by \(|h|\) units.

Here, \(f(x + 5) = f(x - (-5))\), which means \(h = -5\).

Determine the direction and magnitude

Since \(h = -5\), the graph of the parent function \(y = \sqrt{x}\) is shifted \(5\) units to the left.

Answer:

• a. Shift the parent graph 5 units to the right.
• b. Shift the parent graph 5 units to the left. (Correct answer)
• c. Shift the parent graph 5 units upward.
• d. Shift the parent graph 5 units downward.