Question

question 5.
henrietta drew a graph of the function below.
$f(x) = 3\sqrt{x - 4}$
which of the following shows the parent function of henrietta’s graph?
a.
c.
b.
d.

Explanation:

Step1: Identify the parent function

The given function is \( f(x) = 3\sqrt{x - 4} \). The parent function of a square root function of the form \( a\sqrt{x - h} + k \) is \( y=\sqrt{x} \). The parent function \( y = \sqrt{x} \) has a domain \( x\geq0 \) and starts at the origin \((0,0)\) and increases slowly.

Step2: Analyze the graphs

• Option A: The graph does not start at the origin and has a different domain behavior.
• Option B: This is a graph of a relation (not a function) since it fails the vertical line test, and the parent square root function is a function.
• Option C: This is also a relation (fails vertical line test) and not the parent square root function.
• Option D: The graph starts at the origin \((0,0)\), has a domain \( x\geq0 \), and increases, which matches the parent function \( y=\sqrt{x} \) of the given function \( f(x) = 3\sqrt{x - 4} \) (after considering transformations: the given function is a vertical stretch by 3 and horizontal shift right by 4 of the parent \( y = \sqrt{x} \)).

Answer:

D. The graph that starts at (0,0) and increases for \( x\geq0 \) (matching the parent function \( y = \sqrt{x} \))