6-8 Graphing Radical Functions Today’s Objective: I can graph radical functions.
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Transcript of 6-8 Graphing Radical Functions Today’s Objective: I can graph radical functions.
6-8Graphing Radical Functions
Today’s Objective:
I can graph radical functions
Radical FunctionsSketch the graph of
Sketch the inverse graph of
Find the inverse equation of
𝑦=±√𝑥 -5 5-5
5
x
y
x
y
x
y
x
y
Restrict the domain of f to x ≥ 0 𝑓 −1(𝑥)=√𝑥
Radical FunctionsSketch the graph of
Sketch the inverse graph of
Find the inverse equation of
𝑦=3√𝑥-5 5-5
5
x
y
No restriction on the domain.
x
y
x
y
Radical Functions:inverse of power functions
→ Restrict Domain on even degree/index.
𝑓 −1(𝑥)=3√𝑥
x
y
Transformation of
Translation: Vertical Translation: Horizontal
Dilation: Reflections
𝑦=❑√𝑥+𝑘Up k units
Down k units
𝑦=√𝑥−𝑘
𝑦=3√𝑥− hRight h units
Left h units
𝑎>1Stretch:
Compression:𝑦=−❑√𝑥
Across x-axis
0<𝑎<1
𝑦=3√𝑥+h
𝑦=±𝑎 𝑛√𝑥−h+𝑘
x
y
x
y
Across y-axis
𝑦=❑√−𝑥
x
y
x
y
x
y𝑦=𝑎 3√𝑥
x
y
x
y
𝑦=❑√𝑥 𝑦=3√𝑥
𝑦=❑√𝑥
-5 5-5
5
x
y
-5 5-5
5
x
y
Describe the transformation & sketch the graph
𝑦=√𝑥− 2Down 2 units
𝑦=2√𝑥+4Left 4 unitsStretch by 2
x
y
x
y
x
y
x
y
x
y
x
y
x
y
x
y
Horz. Vert.
x
1
4
-15 5
-10
5
x
y
-5 5
-3
7
x
y
-5 5
-3
7
x
y
Describe the transformation, then graph𝑦=√9 𝑥+18
Rewrite function in the form:
𝑦=√¿¿9 2
𝑦=3 √𝑥+2Left 2 unitsStretch by 3
𝑦=3√− 8𝑥−32−2
𝑦=3√¿¿− 8 4
𝑦=− 2 3√𝑥+4 −2Reflect across xStretch by 2Left 4 Down 2
6-8 p. 418:7-19 odds,25-35 odds
-15 5
-10
5
x
y