Question

create a square root function that is vertically compressed by 1/2 and shifted 3 units left.
y = 2√(x + 3)
y = (1/2)√(x + 3)
y = 2√(x - 3)
y = (1/2)√(x - 3)

Explanation:

Step1: Recall transformation rules

For a square root function \( y = \sqrt{x} \), vertical compression by a factor \( a \) (where \( 0 < a < 1 \)) gives \( y = a\sqrt{x} \). A horizontal shift left by \( h \) units gives \( y=\sqrt{x + h} \).

Step2: Apply vertical compression

Vertical compression by \( \frac{1}{2} \) means \( a=\frac{1}{2} \), so the function becomes \( y=\frac{1}{2}\sqrt{x} \).

Step3: Apply horizontal shift

Shift 3 units left means replace \( x \) with \( x + 3 \), so the function is \( y=\frac{1}{2}\sqrt{x + 3} \).

Answer:

B. \( y = \frac{1}{2}\sqrt{x + 3} \)