SM3H Unit 5 Day 3 Notes Graphing Radical Functions

1. Parent Function: The equation of the simplest Square Root Function is Table:

. x

f (x)

Graph:

Domain: Range:

Vertex:

Increasing: Decreasing:

2. Parent Function: The equation of the simplest Cube Root Function is Table:

x

f (x)

Graph:

. Domain: Range:

Point of Inflection:

Increasing: Decreasing:

3. Transformations of Square Root Functions: f ( x) = a b( x − h) + k . The point (h, k) is called the vertex. Transformations of Cube Root Functions: f ( x) = a

a → if 0 < a < 1 , then the parent graph is:

3

b( x − h) + k . The point (h, k) is called the point of inflection. b → if 0 < b < 1 , then the parent graph is:

if a > 1 , then the parent graph is:

if b > 1 , then the parent graph is:

if a is negative, then the parent graph is:

if b is negative, then the parent graph is:

h → h produces a

k → k produces a

For each of the functions, complete the following:

4. f ( x) =

x+3 −2

5. f ( x) = 2 − x + 1

6. f ( x) = 3 x − 2 − 3

7. f ( x) = −3 8 x + 1

Vertex:

Vertex:

Point of Inflection:

Point of Inflection:

Transformations:

Transformations:

Transformations:

Transformations:

Domain:

Domain:

Domain:

Domain:

Range:

Range:

Range:

Range:

Increasing:

Increasing:

Increasing:

Increasing:

Decreasing:

Decreasing:

Decreasing:

Decreasing:

Find the inverse function.

Find the inverse function.

Find the inverse function.

Find the inverse function.