WARM-UP: USE YOUR GRAPHING CALCULATOR TO GRAPH THE FOLLOWING

FUNCTIONS

𝑓 (𝑥 )=√𝑥• Look for endpoints for the graph

• Describe the direction

• What is the shape of the graph?

• What is the domain of the graph?

𝑓 (𝑥 )=3√𝑥• Look for endpoints for the graph

• Describe the direction

• What is the shape of the graph?

• What is the domain of the graph?

GRAPHING AND FUNCTIONS

𝑓 (𝑥 )=√𝑥

•Compare the shape of the graphs of and •Why is the graph of restricted while the graph of is not?

TRANSFORMATIONS WITH THESE GRAPHS

• What does a do to my function?• a- vertical stretch or shrink (if negative, it is a reflection over x-axis) [If 0 < a <

1, then you have a vertical shrink. If a >1, then you have a vertical stretch.]

• What does b do to my function?• b- horizontal stretch or shrink (if negative, it is a reflection over y-axis)

• What does h do to my function?• h- horizontal shift (left or right)

• What does k do to my function?• k- vertical shift (up or down)

EXAMPLE 1: DESCRIBE TRANSFORMATIONS AND GRAPH

• What does the parent graph look like?

• What is a and is it negative?

• What is b and is it negative?

• What is h?

• What is k?

𝑓 (𝑥 )=√𝑥−6

EXAMPLE 2: DESCRIBE TRANSFORMATIONS AND GRAPH

• What does the parent graph look like?

• What is a and is it negative?

• What is b and is it negative?

• What is h?

• What is k?

EXAMPLE 3: DESCRIBE TRANSFORMATIONS AND GRAPH

• What does the parent graph look like?

• What is a and is it negative?

• What is b and is it negative?

• What is h?

• What is k?

𝑓 (𝑥 )=3√𝑥

EXAMPLE 4: DESCRIBE TRANSFORMATIONS AND GRAPH

• What does the parent graph look like?

• What is a and is it negative?

• What is b and is it negative?

• What is h?

• What is k?

𝑓 (𝑥 )=− 3√𝑥

EXAMPLE 5: DESCRIBE TRANSFORMATIONS AND GRAPH

• What does the parent graph look like?

• What is a and is it negative?

• What is b and is it negative?

• What is h?

• What is k?

𝑓 (𝑥 )=√−𝑥

EXAMPLE 5: DESCRIBE TRANSFORMATIONS AND GRAPH

• What does the parent graph look like?

• What is a and is it negative?

• What is h?

• What is k?

𝑓 (𝑥 )=− 123√𝑥−3+2

Homework:Worksheet #11