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

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Answer 1 · 2018-03-19T20:51:59

There is a procedure to graph funcion.

Define the demain and codomain: $RR_+ rarr RR$
Find the intersection between function and x-axes: solve the equation $y=0$ , $x=3$
Calculate the first derivative $y'=-3/(2*√(x-3))$
Calculate $y'=0 rArr$ no solution exist
$(-infty,+infty)$ the slope is negative (the value of the function fall) and never change
Calculate the second derivative: $y'=-3/(4(x-3)^(3/2))$ and $y''=0 rArr$ no solution exist
if $y''>0$ the function is convex (is smiling)
if $y''<0$ the function is concave (is sad)
$y''$ is negative $rArr$ concave

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

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