Section 3.2 Notes

Writing the equation of a function given the transformations to a

parent function

Section 3.2 Notes:

Let f(x) be any parent function. Write the equation for g(x) in terms of f(x) if f(x) is…

translated 5 units left and 2 units up.

5g x f x g x f x 5 2g x f x

Section 3.2 Notes:

Let f(x) be any parent function. Write the equation for g(x) in terms of f(x) if f(x) is…

reflected across the x-axis and horizontally expanded by a factor of .

g x f x g x f x 1

2g x f x

2

Section 3.2 Notes:

Let f(x) be any parent function. Write the equation for g(x) in terms of f(x) if f(x) is…

reflected across the y-axis, vertically expanded by a factor of 3, and translated down 5 units.

g x f x g x f x 3g x f x 3 5g x f x

Section 3.2 Notes:

Let f(x) be any parent function. Write the equation for g(x) in terms of f(x) if f(x) is…

translated right 3 units, up 4 units and

horizontally compressed by a factor of .

3g x f x g x f x 3 4g x f x 5 3 4g x f x 5 3 4g x f x

1

5

Let f(x) be any parent function. Write the equation for g(x) in terms of f(x) if f(x) is…

1. translated right 7 units, down 8 units, and reflected across the x-axis.

2. reflected across both axes and vertically compressed by a factor of .

3. reflected across the y-axis and translated 5 units left.

4. reflected across the x-axis, translated down 9, and horizontally expanded by a factor of 3.

4

5

Answers to practice problems:

1.

2.

3.

4. 19

3g x f x

5g x f x

4

5g x f x

7 8g x f x