Question

question 1
1 pts
given the function $f(x) = -2\sqrt{x + 4}$, identify the y-values for the x-values below.
when $x = -4$, $y = \square$.
when $x = 0$, $y = \square$.
when $x = 5$, $y = \square$.

Explanation:

Step1: Substitute \( x = -4 \) into \( f(x) \)

Substitute \( x = -4 \) into \( f(x) = -2\sqrt{x + 4} \). We get \( f(-4)=-2\sqrt{-4 + 4}=-2\sqrt{0} \). Since \( \sqrt{0} = 0 \), then \( f(-4)=-2\times0 = 0 \).

Step2: Substitute \( x = 0 \) into \( f(x) \)

Substitute \( x = 0 \) into \( f(x) = -2\sqrt{x + 4} \). We get \( f(0)=-2\sqrt{0 + 4}=-2\sqrt{4} \). Since \( \sqrt{4}=2 \), then \( f(0)=-2\times2=-4 \).

Step3: Substitute \( x = 5 \) into \( f(x) \)

Substitute \( x = 5 \) into \( f(x) = -2\sqrt{x + 4} \). We get \( f(5)=-2\sqrt{5 + 4}=-2\sqrt{9} \). Since \( \sqrt{9}=3 \), then \( f(5)=-2\times3=-6 \).

Answer:

When \( x = -4 \), \( y = 0 \); when \( x = 0 \), \( y = -4 \); when \( x = 5 \), \( y = -6 \)