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

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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.

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Radical Functions:inverse of power functions

→ Restrict Domain on even degree/index.

𝑓 −1(𝑥)=3√𝑥

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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

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Across y-axis

𝑦=❑√−𝑥

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y𝑦=𝑎 3√𝑥

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𝑦=❑√𝑥 𝑦=3√𝑥

𝑦=❑√𝑥

-5 5-5

5

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-5 5-5

5

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Describe the transformation & sketch the graph

𝑦=√𝑥− 2Down 2 units

𝑦=2√𝑥+4Left 4 unitsStretch by 2

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Horz. Vert.

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4

-15 5

-10

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-5 5

-3

7

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-5 5

-3

7

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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

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y