Question

which function would produce a shift right of 7 units from $r(x) = -\frac{1}{2}sqrt{x - 7} + 2$? (1 point)

• $w(x) = -\frac{1}{2}sqrt{x - 14} + 2$
• $w(x) = -\frac{1}{2}sqrt{x} + 2$
• $w(x) = -\frac{1}{2}sqrt{x - 13} + 2$
• $w(x) = -\frac{1}{2}sqrt{x - 12}$

Explanation:

Step1: Recall Horizontal Shift Rule

For a function \( y = f(x - h) \), a shift right by \( h \) units occurs. For \( r(x)=-\frac{1}{2}\sqrt{x - 7}+2 \), to shift right 7 units, we replace \( x \) with \( x - 7 \) in the argument of the square root.

Step2: Apply the Shift

Substitute \( x \) with \( x - 7 \) in \( r(x) \):
\( w(x)=-\frac{1}{2}\sqrt{(x - 7)-7}+2=-\frac{1}{2}\sqrt{x - 14}+2 \)

Answer:

\( w(x)=-\frac{1}{2}\sqrt{x - 14}+2 \) (the first option)