Describing Transformed Radical Functions
Describe the transformation of f(x)= 3√(x) -2
Let the graph of g be a horizontal shrink of 1/6 followed by a translation 3 units to the left of the graph of f(x)=√ x
√(6x-18)
(x)1/2=5
x=25
2√(x+1)=4
x=3
4√(x-2)>20
x>27
Describe the transformation of f(x)=√ (x-3) +4
right 3, up 4
Let the graph of g be a horizontal stretch by a factor of 3 followed by a translation 6 units to the right of the graph of 3√ x
3√(1/3x-2)
(2x)3/4+2=10
x=8
√(2x+5)=√(x+7)
x=2
7 3√(x-3) ≥ 21
x≥30
Describe the transformation of f(x)= -3√ (2x)
horizontal/vertical reflection, horizontal shrink by 1/2
Let the graph of g be a reflection in the y-axis followed by a translation 2 up and 1 unit to the right of the graph of f(x)= 2 3√ (x-1)
2 3√ (-x) +2
(8x)4/3+44=300
x=-8,8
5 3√(2x-5) - 10= 15
x=65
3 √(x) -4 ≤ 8
0≤ x ≤ 16
Describe the transformation of f(x)= 3 3√ (x-2) -1
Vertical stretch by 3, right 2, down 1
Let the graph g be a translation 2 units up and 4 units left, followed by a reflection in the y-axis of the graph of f(x)=√(-x)- 1/3
√(x-4) +5/3
(x-7)4=16
x=5,9
x+1=√(7x+15)
x=-2,7 BUT x=-2 is an extraneous solution.
3 √(x-1) ≤ 12
1≤ x≤ 17
Describe the transformation of f(x)= -√ (2x-8) -2
Reflect x-axis, horizontal shrink by 1/2, right 4, down 2
Let g be a vertical stretch by a factor of 2 followed by a reflection in the y-axis and a shift 1 unit up of the graph of f(x)=3 3√ (x+1)
6 3√ (-x+1) +1
(x+30)1/2=x
x=-5,6 BUT -5 is an extraneous solution
√(x+2) +1=√(3-x)
x=-1,2 BUT x=2 is an extraneous solution
4 3√(x+1) < 8
x<7