function math help pls

Question

The point (4,2) is on the parent function f(x)= √x . Determine the new location of this point on the graph. Show your work using the mapping rule. y= -3√1/4(x+1) - 5

Answer 1

y = sqr(x)

x = y^2 is a rightward opening parabola wtih vertex at the origin

y=sqr(x) is the top half of the parabola, where y is always > 0

(4,2) is on the parabola, as 2 =sqr4

y=3sqr((1/4)(x +1)) -5 is the parent semi-parabola shifted down 5, stretched 3/sq4, and shifted left 1. (3,-2) is (4,2) on the transformed parabola half.

2=3sqr((4/4+1) -5

the point (4,2) will become (3, -3( but with a stretching factor)) shift left 1 changes 4 to 3 for the x coordinate. shift down 5 changes 2 to -3. but then stretch the resulting parabola vertically by a factor of 3/2 to get (3,-2)

It helps to graph the parabolas, to see what's going on.