# How do you graph y=-3sqrt(x-3) and compare it to the parent graph?

Mar 19, 2018

There is a procedure to graph funcion.

#### Explanation:

1. Define the demain and codomain: ${\mathbb{R}}_{+} \rightarrow \mathbb{R}$
2. Find the intersection between function and x-axes: solve the equation $y = 0$, $x = 3$
3. Calculate the first derivative y'=-3/(2*√(x-3))
4. Calculate $y ' = 0 \Rightarrow$ no solution exist
$\left(- \infty , + \infty\right)$ the slope is negative (the value of the function fall) and never change
5. Calculate the second derivative: $y ' = - \frac{3}{4 {\left(x - 3\right)}^{\frac{3}{2}}}$ and $y ' ' = 0 \Rightarrow$ no solution exist
if $y ' ' > 0$ the function is convex (is smiling)
if $y ' ' < 0$ the function is concave (is sad)
$y ' '$is negative $\Rightarrow$ concave

The parent graph is c√(a*x+b) where a,b,c are parameters.
a, c tight or strech, b translate the funcion