Question

act math problem set #1
① graph
$y = \sqrt{x}$

Explanation:

Step1: Recall the domain of \( y = \sqrt{x} \)

The square root function \( y=\sqrt{x} \) is defined for \( x\geq0 \) (since we can't take the square root of a negative number in real numbers). So the graph starts at \( (0,0) \).

Step2: Analyze the behavior as \( x \) increases

For \( x > 0 \), as \( x \) increases, \( \sqrt{x} \) also increases, but at a decreasing rate (the function is concave down). For example, when \( x = 0 \), \( y = 0 \); when \( x = 1 \), \( y = 1 \); when \( x = 4 \), \( y = 2 \); when \( x = 9 \), \( y = 3 \), etc. So the graph should be in the first quadrant (since \( x\geq0 \) and \( y=\sqrt{x}\geq0 \)), starting at the origin, increasing slowly, and curving upwards (concave down).

Step3: Sketch the graph (or identify the correct one)

To sketch \( y = \sqrt{x} \), plot key points: \( (0,0) \), \( (1,1) \), \( (4,2) \), \( (9,3) \). Then draw a smooth curve through these points, starting at the origin and increasing with a concave - down shape.

Answer:

The graph of \( y = \sqrt{x} \) is a curve starting at the origin \((0,0)\), lying in the first quadrant, increasing as \( x \) increases, and having a concave - down shape (passing through points like \((1,1)\), \((4,2)\), \((9,3)\) etc.). If choosing from multiple graphs (not shown here but based on the description), the correct graph will be the one that matches this description.