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

##### 1 Answer

Mar 19, 2018

There is a procedure to graph funcion.

#### Explanation:

- 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