Question

graph the function.
f(x) = \sqrt{x + 4}
plot four points on the graph of the function: the leftmost point and three additional points. then click on the graph - a - function button.

Explanation:

Step1: Find the leftmost point

For the square - root function \(y = \sqrt{x + 4}\), the expression inside the square root must be non - negative, i.e., \(x+4\geq0\). Solving for \(x\), we get \(x\geq - 4\). When \(x=-4\), \(y=\sqrt{-4 + 4}=\sqrt{0}=0\). So the leftmost point is \((-4,0)\).

Step2: Find additional points

• When \(x = - 3\):

Substitute \(x=-3\) into the function \(f(x)=\sqrt{x + 4}\). Then \(f(-3)=\sqrt{-3 + 4}=\sqrt{1}=1\). So the point is \((-3,1)\).

• When \(x = 0\):

Substitute \(x = 0\) into the function \(f(x)=\sqrt{x + 4}\). Then \(f(0)=\sqrt{0 + 4}=\sqrt{4}=2\). So the point is \((0,2)\).

• When \(x = 5\):

Substitute \(x = 5\) into the function \(f(x)=\sqrt{x + 4}\). Then \(f(5)=\sqrt{5+4}=\sqrt{9}=3\). So the point is \((5,3)\).

Answer:

The four points are \((-4,0)\), \((-3,1)\), \((0,2)\), \((5,3)\) (you can plot these points on the given graph to graph the function \(f(x)=\sqrt{x + 4}\))