graph the following function by moving the green and blue dots (if necessary). y = 3\\sqrt{x}
graph the following function by moving the green and blue dots (if necessary). y = 3\\sqrt{x}
Answer
Explanation:
Step1: Find the domain
The expression under the square - root must be non - negative. So, for $y = 3\sqrt{x}$, the domain is $x\geq0$.
Step2: Calculate some points
When $x = 0$, $y=3\sqrt{0}=0$. When $x = 1$, $y = 3\sqrt{1}=3$. When $x = 4$, $y=3\sqrt{4}=6$.
Step3: Analyze the shape
The function $y = 3\sqrt{x}$ is a square - root function. The coefficient 3 vertically stretches the basic square - root function $y=\sqrt{x}$. As $x$ increases, $y$ increases, but at a decreasing rate (concave - down).
Answer:
Plot the points $(0,0)$, $(1,3)$, $(4,6)$ and draw a smooth curve starting from the origin $(0,0)$ and extending to the right in the first quadrant since $x\geq0$.