Question

graph the function below by dragging the points.
$g(x) = -3 + \sqrt{x}$
show your work here

Explanation:

Step1: Identify the parent function

The parent function is \( y = \sqrt{x} \), which has a domain \( x \geq 0 \) and starts at \( (0,0) \), with points like \( (1,1) \), \( (4,2) \), \( (9,3) \), etc.

Step2: Analyze the transformation

The function \( g(x)=-3 + \sqrt{x}=\sqrt{x}-3 \) is a vertical shift of the parent function \( y = \sqrt{x} \) down by 3 units.

Step3: Find key points

• For \( x = 0 \): \( g(0)=\sqrt{0}-3 = 0 - 3=-3 \), so the point is \( (0,-3) \).
• For \( x = 1 \): \( g(1)=\sqrt{1}-3 = 1 - 3=-2 \), so the point is \( (1,-2) \).
• For \( x = 4 \): \( g(4)=\sqrt{4}-3 = 2 - 3=-1 \), so the point is \( (4,-1) \).
• For \( x = 9 \): \( g(9)=\sqrt{9}-3 = 3 - 3=0 \), so the point is \( (9,0) \).

To graph the function, plot these points \( (0,-3) \), \( (1,-2) \), \( (4,-1) \), \( (9,0) \) and draw a smooth curve through them, since the square - root function is continuous for \( x\geq0 \).

Answer:

To graph \( g(x)=-3+\sqrt{x} \), plot the points \((0, - 3)\), \((1, - 2)\), \((4, - 1)\), \((9,0)\) (and other points from the square - root parent function shifted down 3 units) and draw a smooth curve through them for \(x\geq0\).