Transformations of Square Root Functions Pt.1
What is the square root parent function?
sqrt(x)
How is
sqrt(x+2)-3
being transformed?
shifted 2 units left and 3 units down.
\sqrt{48}
4\sqrt{3}
Solve
sqrt(7x+1)-8=-2
x=5
Factor
x^2+2x-3
(x-1)(x+3)
How is
sqrt(x)-12
being transformed?
Shifted down 12 units
-4\sqrt(3x - 5) - 2
Vertical stretch by 4, right 5, down 2, horizontal shrink by 3 or 1/3
\sqrt{75}
5\sqrt{3}
Solve:
sqrt(6x-32)+17=21
x=8
\sqrt{x + 5} - 9 = -2
x = 44
How is
sqrt(x)+2
being transformed?
Shifted up 2 units
How is
1/2sqrt(x-1)-3
being transformed.
Vertical Compression of 1/2, shifted right 1 unit and down 3
\sqrt{72x^2}
6x\sqrt{2}
Solve
sqrt(4x+25)-5=-2
x=-4
\sqrt{5x - 4} = \sqrt{3x + 12}
x = 8
How is
sqrt(x-7)
being transformed?
Shifted right 7 units
How is
-5sqrt(x+8)+2
being transformed?
Reflected across the x-axis
Vertical Stretch of 5
Shift left 8 units and up 2 units
3\sqrt{20} + \sqrt{45}
9 x square root 5
Solve
sqrt(4x+1)+8=11
x=2
\sqrt{3x + 10} = x
x = 5 or x = -2
How is
sqrt(x+8)
being transformed?
Shifted left 8 units
How is
sqrt(-1/8x)+1
being transformed?
Reflection across the y-axis
horizontal stretch and shifted up 1 unit
\sqrt{\frac{18x^5}{2x}}
3x2
Solve
6sqrt(x-4)+10=28
x=13
Solve
sqrt(x+12)=x+6
x=-3 or x = -8