## Tutoring on Graphing and Finding Equations of Transformed Square Root Functions

Learning Objectives:

#### Understand to Graph and Solve Equations of Transformed Square Root Functions.

Math Tutoring on Graphing and Finding Equations of Transformed Square Root Functions

The square root parent function is the simplest form of the square root function, or f(x) =√ x.

Parent Function:  f(x) = √x,   x ≥ 0

Vertical Translation: y = √x + d,

d ˃ 0: shifts up I d I units and

d ˂ 0: shifts down I d I units.

Horizontal Translation:  y = √x – c,

c ˃ 0: shifts to the right I c I units and

c ˂ 0: shifts to the left I c I units.

Vertical Stretch and Compression: y = a√x,

1) I a I ˃ 1: vertical stretch,

2) I a I ˂ 1: vertical compression (shrink),

3)  a ˂ 0: reflection in x-axis.

Horizontal Stretch and Compression: y = √bx,

1) I b I ˃ 1: horizontal compression: (shrink),

2) I b I ˂ 1: horizontal stretch,

3) b ˂ 0: reflection in y-axis.

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Hook Questions:

1.    What is meant by a parent function in a square root function?

2.    What is transformed square root function?

3.    What is Vertical or Horizontal Translation in a square root function?

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