1. 6-8 Graphing Radical Functions
Today’s Objective:
I can graph radical functions

2. Radical Functions Sketch the graph of 𝑓(𝑥)= 𝑥 2
Sketch the inverse graph of
𝑓(𝑥)= 𝑥 2
Find the inverse equation of
𝑓(𝑥)= 𝑥 2
𝑦=± 𝑥
Restrict the domain of f to x ≥ 0
𝑓 −1 (𝑥)= 𝑥

3. Radical Functions Sketch the graph of 𝑓(𝑥)= 𝑥 3
Sketch the inverse graph of
𝑓(𝑥)= 𝑥 3
Find the inverse equation of
𝑓(𝑥)= 𝑥 3
Radical Functions:
inverse of power functions
𝑓(𝑥)= 𝑥 𝑛 → 𝑓 −1 (𝑥)= 𝑛 𝑥
Restrict Domain on even degree/index.
𝑦= 3 𝑥
𝑓 −1 (𝑥)= 3 𝑥
No restriction on the domain.

4. Transformation of 𝑓 𝑥 = 𝑛 𝑥
𝑦=±𝑎 𝑛 𝑥−ℎ +𝑘
Translation: Vertical
Translation: Horizontal
𝑦= 3 𝑥
𝑦= 𝑥
Up k units
Right h units
𝑦= 𝑥 +𝑘
𝑦= 3 𝑥−ℎ
Down k units
Left h units
𝑦= 𝑥 −𝑘
𝑦= 3 𝑥+ℎ
Dilation:
𝑦=𝑎 3 𝑥
Reflections
𝑦= 𝑥
Across x-axis
Stretch:
𝑎>1
𝑦=− 𝑥
Compression:
Across y-axis
0<𝑎<1
𝑦= −𝑥

5. Describe the transformation & sketch the graph 𝑦=2 𝑥+4 𝑦= 𝑥 −2
𝑦=2 𝑥+4
𝑦= 𝑥 −2
Down 2 units
Left 4 units
Stretch by 2
Horz.
Vert. x 𝑥 1 4

6. Describe the transformation, then graph
𝑦= 9𝑥+18
𝑦= 3 −8𝑥−32 −2
Rewrite function in the form:
𝑦=𝑎 𝑥−ℎ +𝑘
𝑦= (𝑥+ ) −2 −8 4
𝑦=−2 3 𝑥+4 −2
𝑦= (𝑥+ ) 9 2
Reflect across x
Stretch by 2
Left 4
Down 2
𝑦=3 𝑥+2
Left 2 units
Stretch by 3
6-8 p. 418:7-19 odds, odds