Question

radicals
graphing a square root function: problem type 1
graph the function.
$f(x)=\sqrt{x + 3}$
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 \( f(x)=\sqrt{x + 3} \), the expression inside the square root must be non - negative, i.e., \( x+3\geq0 \). Solving for \( x \), we get \( x\geq - 3 \). So when \( x=-3 \), \( f(-3)=\sqrt{-3 + 3}=\sqrt{0}=0 \). So the leftmost point is \((-3,0)\).

Step2: Find additional points

• Let \( x=-2 \). Then \( f(-2)=\sqrt{-2 + 3}=\sqrt{1}=1 \). So the point is \((-2,1)\).
• Let \( x = 1 \). Then \( f(1)=\sqrt{1+3}=\sqrt{4}=2 \). So the point is \((1,2)\).
• Let \( x = 6 \). Then \( f(6)=\sqrt{6 + 3}=\sqrt{9}=3 \). So the point is \((6,3)\).

Answer:

The leftmost point is \((-3,0)\) and three additional points can be \((-2,1)\), \((1,2)\), \((6,3)\) (you can plot these points on the given graph).