1. Transforming functions
Reflections

2. There are 4 types of function transformations
Translations
Reflections
Rotations
Dilations

3. Reflections in the x-axis

4. Reflections in the x-axis
We are going to graph f(x) and –f(x). I’ve given you –f(x) for the first two, but let’s make sure we agree on what -f(x) is for 3&4.
Graph on calculator then sketch and describe how it moved.
f(x) = 𝑥 2 & -f(x) =− 𝑥 2
𝐹(𝑥)= 2𝑥+3 & −𝐹(𝑥) = −(2𝑥+3)
3) 𝑓 𝑥 = 1 𝑥 and −f x =?
4) 𝑔 𝑥 = 𝑥+1 and −𝑔 𝑥 =?

5. Formalize our rules
For a function 𝑓 𝑥 The function reflects in the x-axis if we multiply the function by -1. Notice: we are multiplying the outputs y, aka the range. If the point (x,y) is on f(x), then the point (x,-y) is on the reflection in the x-axis.

6. Reflections in the y-axis

7. Reflections in the y-axis. What happens if we multiply x by -1?
In other words, we are going to graph f(-x). I’ve given you f(-x) for the first two, but let’s make sure we agree on what f(-x) is for 3&4. (Hint: it could be the same as –f(x), but not all the time.)
Graph on calculator then sketch and describe how it moved.
f(x) = 𝑥 2 & f(-x) =(− 𝑥) 2
𝐹(𝑥)= 2𝑥+3 & 𝐹(−𝑥) =−2𝑥+3
3) 𝑓 𝑥 = 1 𝑥 and f −x =?
4) 𝑔 𝑥 = 𝑥+1 and 𝑔 −𝑥 =?

8. Formalize our rules
For a function 𝑓 𝑥 The function reflects in the y-axis if we multiply our input, or x by -1. Notice: we are multiplying the inputs x, aka the domain. If the point (x,y) is on f(x), then the point (-x,y) is on the reflection in the y-axis.

9. Reflections
With out graphing predict how the following functions will move:
1st I.D. the parent function
𝑦=−3 𝑥 ) 𝑦=− 𝑥
3) 𝑦= −𝑥 4) 𝑦= −𝑥 3

10. Answers: Parent function: 1) 2) 3) 4)
Reflection in which axis? 1) 2) 3) 4)