 ## Presentation on theme: "6-8 Graphing Radical Functions"— Presentation transcript:

Today’s Objective: I can graph radical functions

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

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.

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

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

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